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Articles 91 - 120 of 125

Full-Text Articles in Mathematics

On Quantitative Evaluation Of 3-D Histo-Pathological Images From Confocal Laser Scanning Microscope., P. S. Umesh Adiga Dr. Feb 2000

On Quantitative Evaluation Of 3-D Histo-Pathological Images From Confocal Laser Scanning Microscope., P. S. Umesh Adiga Dr.

Doctoral Theses

Automation of image analysis in the bio-medical ficld is one of the important achievements of applied image processing research. The rapid development in the electronic instrumentation during 1960s and 70s made it possible to automate the routine process of diagnosis and prognosis of many discases. Development of high resolution imaging instruments such as X-ray CT, MRI, etc., for macro imaging and electron microscope, confocal microscope, etc., for micro imaging has given a tremendous boost to the advancement of medical field. Advancement in the field of computing has made it possible to reconstruct the pictures of internal organs of the body …

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Some Contributions To Linear Complementarity Problem., G. S. R. Murthy Dr. Feb 1995

Some Contributions To Linear Complementarity Problem., G. S. R. Murthy Dr.

Doctoral Theses

This dissertation deals with a number of problems related to linear comple- mentarity problem (LCP). Given a real square matrix A of order n and a real n-vector q, the LCP is to find a nonnegative n-vector z such that Az + q 2 0 and zt(Az + 9) = 0. There is vast literature on LCP, evolved during the last four decades. LCP plays a crucial role in the study of mathematical program- ming from the view point of algorithms as well as applications. The inherent nature of the problem has led the researchers to introduce and study a …

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Optimal Leapfrogging, Joel Auslander, Arthur T. Benjamin, Daniel S. Wilkerson Feb 1993

Optimal Leapfrogging, Joel Auslander, Arthur T. Benjamin, Daniel S. Wilkerson

All HMC Faculty Publications and Research

No abstract provided in this article.

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Statistical Analysis Of Economic Activities For Developement In Nepal., Bishnu Pant Dr. Oct 1983

Statistical Analysis Of Economic Activities For Developement In Nepal., Bishnu Pant Dr.

Doctoral Theses

The main objective of this study has been the statistical analysis by the use of those statistical and quantitative tools that could be considered appropriate for applications in an underdeveloped economy, where in usually lies sufficient data and information gaps, towards a proper diagnosis of the problems and prospects of economic activities in its diversified regional environments. This study is conducted with reference to an underdeveloped country, Nepal, where detailed regional analyses have hardly been attempted earlier, to evaluate the regional structures of economic activities for the purpose of clarifying oar visions for a proper kind of regional planning. Though …

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Contributions To The Study Of Bayes Estimates: The Maximum Likelihood Estimate And Rao's Test., S. N. Joshi Dr. Jun 1983

Contributions To The Study Of Bayes Estimates: The Maximum Likelihood Estimate And Rao's Test., S. N. Joshi Dr.

Doctoral Theses

This the sis consists of two parts. In part I we have investigated problems concerning Bayes estimates, especially ex pansion of the integrated risk of the Bayes estinate (also referred to as the Bayes risk or the integrated Bayes risk), approximation of the Bayes estimate and expansion of the posterior distribution. In part II we have introduc ed a new opimun property for estimates and have concluded that the maximum likelihood estimate (m.1.e.) enjoys this property ; in this part we have also investigated what is known as Raos conjecture which saya that the test based on the score function …

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Optimal Strategies Under Superpopulation Models., V. R. Padmawar Dr. Feb 1983

Optimal Strategies Under Superpopulation Models., V. R. Padmawar Dr.

Doctoral Theses

Though the concept of survey sampling is very old and has alvays been in vogue 1t in only during the thirties and forties that a nore syatenatis developnent of the theory of sample surveyo tock place vith the introduction of ideas 1ike sapling without replacenent, probability sapling and stratification. Howovcr, a large nunber of tochniques developad and practiaud during this pariod had nostly edther empirical or intuitive basdo. It usa nuah later that attention vas paid to the purely theörotioal aspect of the dovelepmont of the survey ascipling.The Main problem of sipling tron finite populatian conalata of devising an appropriate …

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Study Of The Robustness Of Inference Procedures In Linear Models With Specification Errors., Thomas Mathew Dr. Feb 1983

Study Of The Robustness Of Inference Procedures In Linear Models With Specification Errors., Thomas Mathew Dr.

Doctoral Theses

We consid er the poneral lingar nodel Y = X v e, here Y io an nx1 rundor voctor taking valacs in 2, x is an nXu ratrix (the deni gn ratrix), ip an 1X1 vectur uf unknown partro tere varying in R and 1s an nx1 voctor of errors with E(e) = 0 and E(ee') - o2v,o2 boing a positive scalar (known or unknown) and is an nXn non-negative definite Ta trix. It in assurmod that n < n. Such a nodel (also known as the Gauss-Markov nodel) is usually denoted by (Y, Xβ,α2v). he defini tions ot un catinable lincar paranctric function, sinple least squires estimator (SLSE), best linear unbia sed estinator (BLUE), linsar ninir:un bias cstinator (IIMBE) and best Iinear nininum bias estinator (BIIMBE) under the nodel (Y, Xβ,α2v arc we 11. known and we retor to Rao and Mitra (1971, Chaptere 7 and B) for the details.Early contributions towärde estinating linear functionals of β are due to Logenire (i806), Gauss (1609) and Varkov (1912), where attention was concentrated on the case where R(X)= n and V = I, the identity natrix. Aitken (1934) considercd the problen of bost lincar unbianed catiration under the setup vhere R(x) = n and V is any positive definite natrix. Bose (1944) conside the casc where R(X) < n and V = 1, while Rao (1945) genera d this to any positive defini te V. Seal (1967) ives a good histo- rical account of the linear model upto 1935 and Plackott (194 9) givus a shorl histurical nute un the raothori uf Jount aquarce. WEE the covariance atixv is nunaingnlar ilh v is nunainglar . la V known und tiho nXn 15 Lrix X is of tnll ruk, i.c. o? runit n and when fur thor the culca ut the ratri are li orthonor- Lial igenvectcre ut v, tun it is at yasil wririahle fact that ie icontical1 ita its S13. his ract was first pointed aut by Andernon (1948) and nutice of it was lakon soon af ter by Durbir und watecn (1950). Fro thin tire cnards, the problen of deriving necessary and sufficient conditions under which the SISE't are e also corresponiing ELUE a hae received con- siderable attontion, mainly due to the norputationl advantage of the S1.SR over the ILUE. The present work is devoted to the study of the robuatness of cstiration and testiag: prucordarcs in linar codels with in- correct desim und dispersion aaa brices. Betore giving a surary of the probleris considUred we shull prosent a brief rovicw of th 1iterature in this area.A atatonant on vorious noceary anl nfricient ountitionn for the equalily of tha iaa aid correapotsiin BIJRse de by Zyakind (1962) On: of the cunlatiuna ota tod huru 1a that thore exista a nahuut of r udiponveetoro of V that forma banio uf the vector spucu spied by tho colunna of the design ratrix X. A proot thut the cáguvuotur ounition is both neoessary and auf- firient for the correapuiliny HTE arsl SLSE to huve the ae cuvarianeu natri: du oresoutua vdth X n all at ai 7 aonningular hy Ma, maa ant aGuáro (1962).

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Economic Regionalization Of India 1960-61 And 1970-71., Rabindranath De Dr. Feb 1982

Economic Regionalization Of India 1960-61 And 1970-71., Rabindranath De Dr.

Doctoral Theses

A massive investment programme has been undertaken in India through the process of planning. But the effects of such investment on economic growth are worked out only at the aggregate level for the country as a whole; its contribution to the growth of the different regions in the country is yet to be adequately understood. Now, for a large country like India with significant regional disparities in the level of living, an essential objective of development policy should be to reduce the existing economic inequality between the regions | in particular, the inequality in the level of living. The priority …

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Estimation In Errors-In-Variables Models., Manoranjan Pal Dr. Feb 1982

Estimation In Errors-In-Variables Models., Manoranjan Pal Dr.

Doctoral Theses

In many econometric investigations, the 'errors-in variables' (EIVs) are not negligible (Morgenstern, 1963). Examination of 25 series relating to national accounts by Langaskens and Rijekeghan (1974) showed that the standard deviations of the errors ranged from 5 to 77 per cent of the average value of the corresponding variable. Such errors may vitiate least-squares (LS) estimation of regression coefficients (Johnaton, 1972). The well-known methods (ML; IV, including grouping method) proposed for handling classical EIV model (EMM) in regression analysis muffer from serious linitations. Same of them make strong distributional assumptions about the errors (and the regressors) and/or assume prier knowledge …

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On Specification And Statistical Inference In Single Equation Regression Models., Nityananda Sarkar Dr. Feb 1982

On Specification And Statistical Inference In Single Equation Regression Models., Nityananda Sarkar Dr.

Doctoral Theses

This thesis attempta to cansider and provids solutions to viat nay be broadly decribed na Bone problems of speciification and satatistical inforence in single equation lineur regression models. It co sists of three parte, each having several chepters. The firat part in devoted to sme problems connec ted vith the use of the wall-imown Bor-Cox (BC) tranaformation of variablee in single equetion ragreanion nodels. In the other two parts we exanine an autocorrelated linear regreasion nodel from a rather unconventional angle. Precisely, we consider the problema which arise when the error tem in an autocorre lated linear regression nodel is …

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Asymptotic Expansions And Deficiency., Tapas Kumar Chandra Dr. May 1981

Asymptotic Expansions And Deficiency., Tapas Kumar Chandra Dr.

Doctoral Theses

The efficiencies intmduced by B.J. G. Pitnan and R. R.Bahadur are both meant to compare the asymptotie perfornance or statistical procedured. However there are nany interesting situations where these eriteria prove inadequate and rurther discrimination 1s necessary. One such attempt of furthor refinenent is the criterion of defieieney.This investigation was undert aken with the ob ject of davelop- Ing tools for studying defieiency of test proceduros vith (1) same Pitman efficieney, OT (11) sane Bahadur efficiency.Deficiency in the first case has been defined by Hodges and Lehumann (1970). Deficiency in the second case vas defined by Chandra and Chosh (1978). …

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Role Of Labour In Indian Agriculture., Manabendu Chattopadhyay Dr. Apr 1981

Role Of Labour In Indian Agriculture., Manabendu Chattopadhyay Dr.

Doctoral Theses

In this stuly, we have analysed some aspects of labour condi- tions and relations in Indian agriculture on the ba si s of available secondary source data.We have started our analysis by taking a look at the origin and growth of the class of agricul tural labourers in the Indian society. Possible explanations for the ori gin and growth of the agricul tural labour class have been reviewed in this context. We then prmceed to examine the trends in employment and unemployment in both the rural and urban sectors of India. The trends are studied in terms of absolute nurbers …

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Flow-Shop Scheduling Problems., N. R. Achuthan Dr. Mar 1981

Flow-Shop Scheduling Problems., N. R. Achuthan Dr.

Doctoral Theses

Researchers attention was drawn to the study of schodulirg problems through mathemtical modelling, probably for the first time, when Johnson (1954) publishod his famous paper in mval research logistic quarterly. Thercafter, mny authors have contimued to contribute to the growth of the theory of scheduling. A vast colloctim of papers related to this area is rogularly published by journals like mamgement science, operations research, operational research quarterly, naval research logistic quarterly, opsearch etc.. A good grasp of the litermture in this arca can be had from the books by Conway et al. (1967), Baker (1974) and Rinnooy Kan (1976).This thesis …

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Asymptotic Theory Of Extimation When The Limit Of The Log-Likelihood Ratios Is Mixed Normal., P. Jeganathan Dr. Feb 1981

Asymptotic Theory Of Extimation When The Limit Of The Log-Likelihood Ratios Is Mixed Normal., P. Jeganathan Dr.

Doctoral Theses

In one of his fundamental papers Le Can (1960) introduced what is now called locally asymptotically normal (LAN) families of distributions and obtained several basic results regarding the asymptotic theory of estimation and testing. Roughly speaking, a sequence of families is said to satisfy the LAN condition if the corresponding sequence of appropriately normalised log-likelihood function is locally approximated with probability tending to one by the sum of two expressions, the first one being a sequence of rand om linear functions of the normalised parameter and the second one being a non-random quadratic form of the normalised parameter, and the …

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Abo Blood-Group Gene Frequencies In The Indian Sub-Continent: A Statistical Study Of Patterns Of Variation., Partha Pratim Majumder Dr. Feb 1981

Abo Blood-Group Gene Frequencies In The Indian Sub-Continent: A Statistical Study Of Patterns Of Variation., Partha Pratim Majumder Dr.

Doctoral Theses

The main objective of this thesia is to diascover patterns of variation botwoen geographácal regions and socio- religious groups in the Indian sub-continant in respect of the distribution of ABO ganea controlling the O-A-B-AB blood group syston through a comprehensive, unified statistical analysia of all the relevant data avallable táll 1977.The posaibility of uning the 0-A-B-AB blood groupe as a marker for population genctic studias was first discovereda by Dr. and Mra, Hirachteld in 1919. The data collected by tham from amy personnel bolonging to various populatian groupa ahowed clear-cut di frerences and ganerated a lot of interost emong anthropologista, …

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Contractual Arrangements In Agriculture : Some Theory And Empirical Evidence., Chandrasekhar Pant Dr. Feb 1981

Contractual Arrangements In Agriculture : Some Theory And Empirical Evidence., Chandrasekhar Pant Dr.

Doctoral Theses

Tenancy in agriculture is an arrangement between the landowner and tenant in which the tenant paye to the landowner a certain mutually greed sun (or stare) of produce in return for the right to cul ti vate and appropriate the output produced on rentedend. There are different types of tenaney arrangements and often these differences relate to the form of payment of rent. Two of the more prevalent tendancy arrangements are share cropping (or cropshering) sand fixed-rent tendany, Under sh-re- cropping, the rent is a contructed percentage of the output produced on rented land while in a fixed-rent contract the …

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Extended Particles And The Interpretation Of Quantum Mechanics., C. K. Raju Dr. Feb 1981

Extended Particles And The Interpretation Of Quantum Mechanics., C. K. Raju Dr.

Doctoral Theses

A now fornulation of the problen of junotion condiiions 1a given, It is pointed out that, if the existing the ory of relativity ie to be consistent with the existence of natter in the form of particles, thon the cannot be continuously aifferentiable everywhere, The mathonatical part of the problem of Junction conditiona is solved by using nonatandard analysis to define prod uo ta and compoaitions vith distributiona, The definitiona are auch that o ontimaed belief in the equations of relativity is justified, As an application, the equations of IRotion for the apherically-synne tric surface layor, at the Schwerzachild-Minkowsici junction, …

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Studies In Multipartite Self-Complementary Graphs., T. Gangopadhyay Dr. Feb 1981

Studies In Multipartite Self-Complementary Graphs., T. Gangopadhyay Dr.

Doctoral Theses

The class of self-complenentary egraphs has been extensively etudied by nany people, among others by C.R.J. Clephan, S.B, Rao, G, Ringel and H. Sache, and nany problems have been solved for this class, such as the Haniltonian problen and the characterisati on of potentially and forcibly self-complenentary dogree sequences (see [1], [2], [12), [13), [14, [15)). Thus self-complenentary graphs form an interesting class and this has been generalised by Hebbare [8] into the class of multipartite self-conplementary graphs.An r-partite self-complenentary graph is an r-partite graph G which is isomorphic to its r-partite complement where H has the sane vertex set …

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Some Asymptotic Properties Of Maximum Likelihood Procedures., Kasala Subramaniam Dr. Jun 1980

Some Asymptotic Properties Of Maximum Likelihood Procedures., Kasala Subramaniam Dr.

Doctoral Theses

This thesis consists of two parts dealing with maximum likeli. hood procedures in two different frameworks. In the first part (Chapters 1,2 and 3) we consider inference about a parameter which is discrete or separated in the sense that no f(x, e) can be obtained as a "limit" of ff(x,e1)}, + e. (A precise definition of what is meant by & "limit" is given in Chapter 1). In the second part (Chapters 4 and 5) we consider the usual eÅŸtimetion problem of what may be called in constrast to Part I, a contimuous parameter. We assume, we have an exponential …

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Some Problems On Econometric Regression Analysis., Maitreyi Chaudhuri Dr. Feb 1980

Some Problems On Econometric Regression Analysis., Maitreyi Chaudhuri Dr.

Doctoral Theses

Very often in eoonometrio enslysis one adopts the classical lineer regression model. The classical linear regression model is given by If, in addition, e is assumed to be normally Ä‘istributed, the model is called classical normal1 linear regression mode1.Ordinary least squares (0LS) methods of estimation and hypothesis testing are besed on this ndal, d eveluton copy of CV POFO But the assumptions on É›is and- xs may not be fulfilled in reality; or, in other words, the model may not be correctly specified. Cne class of problems arises when some of the regressors are omitted from the equation and/or scme …

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Geological Depletion And Locational Advantage In The Analysis Of Mineral Extraction Programmes., Sudhir Dattatray Chitale Dr. Feb 1980

Geological Depletion And Locational Advantage In The Analysis Of Mineral Extraction Programmes., Sudhir Dattatray Chitale Dr.

Doctoral Theses

The aim of the study is to evolve optimal pro- duction and linkage plans, to meet and oxogenously specified, spatially distributed time profile of damands from a set of spatially dispersed coking coal bearing geological blocks. The plans are optimal in the sense of minimun discounted present value of the sun of production, washing and transport costa.Pocussing our attention on a geological block consisting of many coal seams, we work with it as if it was operated as one production conplex. Geological depletion in ea ch block is formalised by estimat ing a Block Level Cumulative Cest Function (BLCCF) based …

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On Some Non Uniform Rates Of Convergence To Normality With Applications., Ratan Dasgupta Dr. Feb 1980

On Some Non Uniform Rates Of Convergence To Normality With Applications., Ratan Dasgupta Dr.

Doctoral Theses

We obtain non-uniform rates of convergence to normality of the partial sums in a triangular array of random variables, where variables in each array are independently distributed. Section 2 of this chapter generalizes the results of Michel (1976) mainly in the direction of considering a triangular array of rand om variables. A slight generality in the moment assumptions is also made. The later extension is quite in spirit with Katzs (1963) extension of the classical Berry-Esseen theorem. Since by Tomkins theorem (see Tomkins (1971) or Stout (1974)) the laws of the iterated logarithm are directly related to the zone where …

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On The Asymptotic Theory Of Quantiles And L-Statistics., Kesar Singh Dr. Jun 1979

On The Asymptotic Theory Of Quantiles And L-Statistics., Kesar Singh Dr.

Doctoral Theses

Let {Xi} be a sequence of r.v.s. nth stage we At the define e.d.f. as Fn (x) = (# Xi, ≤ x :≤ i ≤ n)/n and the ttn sample quantile as Qnt = inf {x : Fn (x) ≥ t} for t > 0 and = en(0+) for t=0. Most of the techniques of studying the process Qnt: 0 ≤ t≤ 1} consist of relating {Qnt} with some suitable linear statistics. The following are some of the commonly used methods for studying quantiles :(i) The Direct Methods In The Independent Case. Here, one can actually find the exact dis tribution …

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A Study Of Admissibility Through Exterior Boundary Value Problem., C. Srinivasan Dr. Jul 1977

A Study Of Admissibility Through Exterior Boundary Value Problem., C. Srinivasan Dr.

Doctoral Theses

The study of admissible decision procedures began in late forties when Wald introduced the concept to characterize the minimal complete class of decision procedures. Starting with the pioneering work of Abraham Wald, there has been considerable contribution to this area over the last three decades. However, most of the articles in this field dealt with specific decision procedures arid studied their admissibility. It was Stein [11 who first characterized, admissible decision procedures. Farrell ([2], (3]) generalized the result of Stein. In spite of the works of Stein and Farrell the problem of deciding whether a given decision procedure is admissible …

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Employment And Output Objectives In Project Selection., Basudeb Sen Dr. Feb 1976

Employment And Output Objectives In Project Selection., Basudeb Sen Dr.

Doctoral Theses

Alarmingly high and increasing rates of unemployment among the fast growing labour force has, in the recent years, becmne a serious threat to the social, political and economic envirorment in developing countries like India. Despite planned efforts at economic development, the percentage of unemployed in the labour force is estimated to have increased fron 9.0 per cent in 1962 to 1o.4 per cent in 1971 and 11.0 per cent in 1972 Dutt and Sundharam (1975) 7. Eradication of unemployme nt through creation of large-scale job opportuni ti es has come to establish itself as a major objective of the country. …

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Some Combinatorial Arrangements And Incomplete Block Designs Through Them., Anis Chandra Mukherjee Dr. Feb 1975

Some Combinatorial Arrangements And Incomplete Block Designs Through Them., Anis Chandra Mukherjee Dr.

Doctoral Theses

The use and importance, in Statistical Experimental, of Incomplete Block Designs, particularly, Balanced Incomplete Block (BIB) Designs, Doubly Balanced Incomplete Block (DBIB) Designs and Partially Balanced Inçomplete Block (PBIB) Designs are well known. Several combinational arrangements, including the incidence matrices of these Incomplete Block Designs and association matrices associated with PBIB Designs are known to be of use in Design of Experiments. In this thesis, we consider the construction problems pertaining to some of these combinational arrangements and take up the problem of construction of BIB, DBIB and FBIB Designs through them. The combinational arrangements studied in the thesis have, …

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On Some Problems Of Sequenting And Grouping., T. S. Arthanari Dr. Feb 1975

On Some Problems Of Sequenting And Grouping., T. S. Arthanari Dr.

Doctoral Theses

The problems of sequencing arise in almost all walks of life. Theory of scheduling deals with such problems. Usually, these probl ems are stated in the literature in terms of jobs, machines, operations, penalties, due dates et cetera, that is, in the language of machine shops. The real life problems of In machine - shop job sequencing are of a complex nature. general, we consider processing n items on a certain group of machines, so as to optimize certain objective, subject to various cons traints on precedence, machine availability, due date and so on. The job sequencing problems are includ …

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Contributions To Methodology Of Construction Of Consistent Index Number., Dodla Sai Prasada Rao Dr. Feb 1973

Contributions To Methodology Of Construction Of Consistent Index Number., Dodla Sai Prasada Rao Dr.

Doctoral Theses

International variation in national product is a subject of considerable interest, and any meaningful comparison of national product or per capita national income has to be in termo of a common currency. An intertemporal comparison for the same country at two points of time is mote meaningful in real terms, or in other words when the currency unit is adjusted for change in the general price level between the two points of time. In the same manner, the level of output or of consumption of a group of persons belonging to a region or to a particular socio-economio group can …

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Some Contribution To The Theory Applications And Computations Of Generalized Inverses Of Matrices., Pochiraju Bhimasankaram Dr. Feb 1972

Some Contribution To The Theory Applications And Computations Of Generalized Inverses Of Matrices., Pochiraju Bhimasankaram Dr.

Doctoral Theses

The origin of the concept of a generalized inverse dates back to as early as 1920 when Moore defined the generalized inverse of matrix which is equivalent toDefinition 1 (Moore) : Let A be a m >< n matrix over the field of complex numbers. Then a is the generalized Inverse of A if AG is the orthogonal projection operator projecting arbitrary vectors onto the column space of A and GA is the orthogonal projection operator projecting arbitrary sectors onto, the column space of G.Mod re (1935) discussed this concept and its properties in some detail. Tsong (1949a, 1949b, 1956) discussed about generalized 1nverses of operators in more general spaces and Bjerhammer (1951) discussed the generalized inverse of a matrix in connection with an application to geodetic calculations. Unaware of the work of Hoore and others, Penrose (1955) defined a generalized inverse of a matrix as follows :Definition 2 (Penrosel) : Let A be a m *n -matrix over the field of complex numbers. Then G is a generalized inverse of a if (i) AFA= A; (ii) GAG=G; (iii) (AG)*=AG and (iv) (GA)*-GA.Penrose (1955,1956) showed that for every matrix there exists a unique generalized inverse, discussed several of its important properties, gave applications to solution of matrix equations and suggested a practical method of computation of the generalised inverse.As was pointed out by Rado (1956) Moo res definition of generalized inverse is equivalent to that of Penrose, Such generalized inverse is called the Moore-Penrose inverse and A is used to denote the Moore-Penrose inverse of A.Rao (1955), unaware of the earlier or contemporary Work, constructed a pseudo-inverse of a matrix which he used in some least squares computations, In a paper in 1962, he defined a generalized inverse (g-inverse) as follows, proved some interesting properties and gave applications of g-inverses to Mathomatical Statistics.Definition 3 (Rao) : Lot A be am x n matrix, Then a n >< m matrix. Then a n >< m matrix G is a g-inverse of A if x = Gy is a solution of the linear system Ax = y whenever it is consistent.A g-inverse if u matrix (in the sense of Rao) is in general not unique, As 1s easily observed (from definitions 2 and 4) the class of all g-inverses of a matrix A contains A*. Rạo (1965, 1967) developed a calculus of g-inverses, classified the g-inverses according to their use and according to the proporties they possess similar to those of the inverse of a nonsingular matrix and suggested further applications to Mathematical Statistics. Mitra (1968a, 1968b) gave an equivalem definition of a g-inverse, developed further calculus of z-inverses, used g-invorses to solve some matrix equations of interest and explored the possibilities of some new classes of g-inverses with applications. In a series of papers, and a monograph Mitra and Rao (1968, 1970) pursued the research on generalized inverses of matrix's and their applications to various scientific disciplines.

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Optimum Estimators And Strategies In Survey Sampling., M. K. Ramakrishnan Dr. Feb 1971

Optimum Estimators And Strategies In Survey Sampling., M. K. Ramakrishnan Dr.

Doctoral Theses

This thesis consists of nine chapters. In the first chapter we give the basic concepts and definitions and also a broad review of the literature related to the problems considered in this thesis. The second and third chapters are devoted to a detailed modified comparison of sampling with and without replacement, for the case of equal and unequal probability sampling respectively. In the fourth and fifth chapters we discuss the criteria of hyper-admissibility and linear suf2iciency for the choice of an optimum estimator for a given sampling design. The succeeding three chapters have as their main objective the central problem …

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