Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
Articles 31 - 60 of 79
Full-Text Articles in Physical Sciences and Mathematics
On Logistic And Some New Discrimination Rules:Charecterizations,Inference And Application., Supratik Roy Dr.
On Logistic And Some New Discrimination Rules:Charecterizations,Inference And Application., Supratik Roy Dr.
Doctoral Theses
Introduction and Summary Consider the problem of classification of an observation into one of two specified populations. Fisher's classification rale, just as several other rules commonly used in practice, depends only on the ratio of the individual densities fi(x), i = 1,2. This led Cox (1966),/27) to model the "posterior odds" by a simple function. Specifically,Cox's logistic discrimination (LGD) rule is then based on the statistic a + 'ßx. This has the advantage that individual densities f.(x) need not be known and we only need to estimate the parameters a and B.Another advantage, which is claimed , is that the …
Generalised Bootstrap Techniques., Singdhansu Bhusan Chatterjee Dr.
Generalised Bootstrap Techniques., Singdhansu Bhusan Chatterjee Dr.
Doctoral Theses
A typical problem in statistics is as follows: there is some observable data Xn = (X1,..., Xn), and a parameter of interest θ which is related in such a way to the distribution of Xn that meaningful conclusions about θ can be drawn based on Xn. Sometimes data Xn is observed keeping the objective parameter θ in mind, at other times the parameter appears while trying to model the observed data.Once the data is observed and the parameter fixed, the questions that have to be addressed are as follows:(I) How to estimate θ from the data Xn?(II) Given an estimator …
On Measuring The Cost Of Children:The Case Of Rural Maharashtra., Manisha Chakrabarty Dr.
On Measuring The Cost Of Children:The Case Of Rural Maharashtra., Manisha Chakrabarty Dr.
Doctoral Theses
In this dissertation we have attempted to measure the cost of children, which plays a crucial role in matters relating to welfare and public policy like child benefits and compensation policies of the government. The cost is measured based on the single equation as well as the systems approach using the 38th round National Sample Survey (NSS) data on household consumer expenditure for rural Maharashtra (relating to the period of January to December, 1983).The first chapter provides a brief account of the basic literature on empirical demand analysis which is relevant for welfare comparison between households. To be specific in …
Engel Curve Estimation From Budget Data Relating To Short Reference Periods., Suchismita Ghosh Dr.
Engel Curve Estimation From Budget Data Relating To Short Reference Periods., Suchismita Ghosh Dr.
Doctoral Theses
The main motivation of the present dissertation is the estimation of engel elasticities of certain items of consumption after eliminating the possible effects of seasonal and other short-run fluctuations from household budget data. Indian budget data provided by the National Sample Survey Organization (NSSO), mainly relating to the 38th round (January - December, 1983), has been utilized for the study. Such data generally relate to a moving reference period of 'last 30 days' preceding the date of interview (also referred to as the last month reference period). The use of such a reference period introduces errors in observation in both …
Muyltivariate And Regression Analysis Based On The Geometry Of Data Clouds., Biman Chakraborty Dr.
Muyltivariate And Regression Analysis Based On The Geometry Of Data Clouds., Biman Chakraborty Dr.
Doctoral Theses
Median is a natural estimate of location of a data set, and there are several versions of inultivariate median studied in the literature, each of which is an interesting descriptive statistic for multivariate data and provides some nice geometric insights into the data cloud. One would expect that multidimensional median will be a natural estimate for the center of symmetry of a multivariate distribution. However, there is no unique concept of symmetry in multivariate problems. The center of symmetry can be defined in several ways there. For example, the d-dimensional random variable X is spherically symmetric about e €Rd if …
Static Interconnection Networks And Parallel Algorithms For Efficient Problem Solving., T. Krishnan Dr.
Static Interconnection Networks And Parallel Algorithms For Efficient Problem Solving., T. Krishnan Dr.
Doctoral Theses
There is nothing more difficult to take in hand, more perilous to conduct, or more uncertain in its success, than to take the lead in the introduction of a new order of things.
Asymptotic Properties Of Posterior Distributions And Study Of Some Nonregular Cases., Subhashis Ghosal Dr.
Asymptotic Properties Of Posterior Distributions And Study Of Some Nonregular Cases., Subhashis Ghosal Dr.
Doctoral Theses
The asymptotic approach to statistical estimation is frequently adopted be cause of ita general applicability and relative simplicity. The modern study of asymptotic theory, initiated in Le Cam (1953), has undergone a vigorous devel- opment through the classic works of Le Cam, Hájek, Bahadur, Ibragimov and Has'minskii (Khas'minskii), Bickel, Pfanzagl, Millar and many other scholars; see Le Cam (1986), Le Cam and Yang (1990), Ibragimov and Has'minskii (1981) and the review article by Ghosh (1985) for an account of this development.Most of the results in asymptotic theory of estimation are obtained under the classical Cramér-Rao type regularity conditions or their …
Some Limit Theorem On Conditional U-Statistics And Censored Data Non Parametric Regression., Arusharka Sen Dr.
Some Limit Theorem On Conditional U-Statistics And Censored Data Non Parametric Regression., Arusharka Sen Dr.
Doctoral Theses
In Statistics, a classical problem is that of estimating the regression function which is defined as m{t) := E(Y|X = ), te R, for two random variables X and Y such that EY < 0o. The estimators are constructed iased on a sample {(Xi, Yi.)}, 1sis n,n 2 1, from the distribution of (X, Y). Throughout this thesis, we assume X and Y to be real-valued for the sake of convenience. The classical approach to this problem is to assume a parametrized, polynomial form for nt-), i.e., m(t) := Bo + E-1 P,ti, p 21, and obtain estimates of the unknown paraineters Bo, Bj,, 1sjsp. Later, with the development of techıniques for non-parametrie density estimation, it was sought to extend these techniques to regression estimation. Heuristically, the two problems can be seen to be related as follows : let fi(-) be the marginal density of X and note that E1(X S x) = h(t)dt, z € R, whereas EY 1(X Sx) = m(t)fi(t)dt, x E MR. (1.0.2) In other wordds, (1.0.1) can be looked upon as a special case of (1.0.2), with Y = 1. + similarity, as we shall see later on, has been the underlying theme in Chapters 2 and 4 of the present work.) The following non-parametric regression estimator was proposed independently by Nadaraya (1964) and Watson (1964): "(): := m.(Y,)/m.(1, ), te R, (1.0.3) where m,(Y, t) = (nan)- E-, Y;K((t - X:)/an). (1.0.4) m,(1,1) (na,)-E, K((I - X)/a,). Here K(), the so-called kernel function, is chosen to satiafy various analytical conditions (typically, K(-) is taken to be a density function), and a, 1 0 are the bandwidths which go to zero sufficiently slowly (e.g., na,0o as n00) in order to ensure consistency of the estimator mW (). The intuition behind such an estimator is that m,(Y,) is an estimator of mt-)fi() while m,(1,) cstimates the density fa(-). See Prakasa Rao (1983), Chapters 1-4. for an introduction to non-parametric density and regression estimation. Now, m(t) is a functional of the conditional distribution of Y, given X = t. A natu- ral generalisation of the regression estimation problem seems to be the estimation of the following functionals: mh(t1,....tk) := E{h(Y1,.....Yk) | X1, = t1.,Xk. = tk), (t....) € R*, k 2 1, (1.0.5) where h: R*- R is such that Elh(Y...., Y) < 0. A similar generalisation led Hoelfding (1948) from the sample mcan to the theory of so-called U-statistics, in the uncondilional set-up. The estimation of (1.0.5) were considerexl, for the first time in published form, in Stute (1991) where the following conditional U-statistics were proposed as estimators;where Fn(-) := n-1E, 1(Xi; < ) denotes the empirical distribution function (c.d.f Bochynek discussed the asymptotic normality of conditional U- and V-statistics and pei formed simulation studies on them. Stute (1991) established weak and strong pointwis consistency and asymptotic normality of U(t). Liero (1991) studied uniform strong con sistency of conditional U-statistics and established asymptotic normality of the integrate squared error (ISE) statistic:for suitable A c R* and weight function w(-). We quote the following examples to illustrate the possible use of conditional U-statistics See Stute (1991) and Bochynek (1987) for other examples. Throughout this thesis, our set up will be as foliows: {(Xn, Yn)}n>ı is a bi-variate i.i.d sequence, with (X1, Y1) having join density f(,-) and X, having marginal density fi(-). Consequently,
On Some Problems In Analysis Of Covariance Structure., Sadhan Samar Maiti Dr.
On Some Problems In Analysis Of Covariance Structure., Sadhan Samar Maiti Dr.
Doctoral Theses
In recent years, the teahniques of struotural analynie of covarianoe and correlation matrioes have frequently be en employed espeed ally in the s ooial and behavioural soieno es for analysing multivariate data. Analysis of covarlance structures (ACOVS) lea; generie tem describing a variety of statistioal procedures for testing and measuring the goodnese-of-fit of certain types of struotures postulated a priori for the cova- riance matrix by plaoing al temative restriotione on the para- neter natrioes of the general model" [Mukherjee, 1976, p. 132].The aoronyn AOOVS' standa for; analyeis of covarianoe atructurea; and waa firat proposed by Book (1960) as a …
On Image Information Measures And Object Extraction., Nikhil Ranjan Pal Dr.
On Image Information Measures And Object Extraction., Nikhil Ranjan Pal Dr.
Doctoral Theses
The field of image processing deals with the manipulation of data which are inherently two-dimensional in nature. techniques of image processing sten from two principal application The areas, namely, Improvement of pictorial information for human interpretation and processing of scene data for automatic machine perception. These areas together have experienced a vigorous growth in recent years because they have offered a number of important applications in solving scientific and engineering problems. In biological and medical sciences, we are interested in automatie analysis and interpretation of radiographs, cell images micrographs. In netallurgical, geological and and tissue environmental sciences, we are concerned …
Search Designs And Other Topic In Fractional Replication., Kashinath Chatterjee Dr.
Search Designs And Other Topic In Fractional Replication., Kashinath Chatterjee Dr.
Doctoral Theses
This thesis primarily deals with search designs (see Srivastava (1975)) of various types for general symmetric and asymmetric factorials. The thesis also considers some other types on fractional factorials. We have made use of Kronecker products and various other results from matrix theory.In the first four chapters, different types of search designs have been studied. Chapter 5A considers the construction of orthogonal main-effect plans for general factorial experiments under the presence of a linear time trend. Chapter 5B extends the calculus for factorial arrangements to a fractional factorial set-up and examines critically the proportional frequency plans from the point of …
Contribution To The Theory Of Stochastic Games., Sagnik Sinha Dr.
Contribution To The Theory Of Stochastic Games., Sagnik Sinha Dr.
Doctoral Theses
A mathematical theory of Games of Strategy was born in several stages between 1928 and 1941. John von Neumann is known as its father. The culmination of the pioneering work of von Neumann and Morgenstern was the publication of the Theory of Games and Economic Behavior (Ref.28] in 1944. Ik is snid of the book . posterity may regard this book as one of the major scientifie achievements of the first half of the twentieth century. Emphasizing a new approach to competetive behaviour through a mathematical reduction to suitable games of strategy, this giant work laid bare a host of …
Some Contributions To Directional Statistics: Characterixation And Asymptotics., Sumitra Purkayastha Dr.
Some Contributions To Directional Statistics: Characterixation And Asymptotics., Sumitra Purkayastha Dr.
Doctoral Theses
In many natural and physical sciences the obser- vations are in the form of directions in 2- or 3-dimensional Euclidean space or rotations of such a space. In the former case, it is tustomary to represent the observations by points on the unit ball in R2 or R3, or more.generally, Rp. In the latter case, the observations are represented by orthogonal matrices having determinant +1, or more generally, by nxp (ngp) matrices A satisfying AAt=In,i.e., by elements of Stiefel manifold. Examples .of observations on directions in 2-dimensional space include those on wind direction or on flight direction of birds, Similarly, …
Some Contributions To The Asymptotic Theory Of Estimation In Non Regular Case., Tapas Samnta Dr.
Some Contributions To The Asymptotic Theory Of Estimation In Non Regular Case., Tapas Samnta Dr.
Doctoral Theses
The introduction of the concept of onymptotie efficiency of statistical eatimators in connection with proposing and developing she method of maximu, 1ikelihood by . Fislior (Fisher (1922, 1929)) 1s really the atar ting point of the asymptotie theory of es timation. -istorieally, however, Laplace (1774) and Gausa (1009) had made tuo irferent studieo oarlier then Fisher bo ti connected d th as ymp to tie theory of estination. Fisher considered only consistent a symptotically rewnal untinotoro and meured the asyaptotie performance of an anti- mator by ite aayep totle variaree. Thus, a coreistent aeynp to tieally nomal eetimoator with let …
Asymptotic Study Of Estimators In Some Discrete And Continuous Time Model., Arup Bose Dr.
Asymptotic Study Of Estimators In Some Discrete And Continuous Time Model., Arup Bose Dr.
Doctoral Theses
This thesis deals with an asymptotic study of estimatore in some discrete time and continuOus time models.The firet part deele with time eeriee date modelled by moving sverage and eutoregreseive proceseee. Higher order as ymptotioe beyond. as ymptotio normality, of the usual astimatore heve been dealt by Phillipe (1977,1978), Durbin (198o), Oohi (1983), Tanaka (1983), Fujikoshi and Ochi (1984). o(n-1/2) or o(n-1) expenaions ara 'obteined by these authore under the assumption of normality of orrors. The reason for this wes the lack of suitable. expaneions for normalized sums of dependent random vectora. Recently Gotza and Hipp (1983) heve been able …
Estimation Of Demographic Parameters For India., S. Guha Roy Dr.
Estimation Of Demographic Parameters For India., S. Guha Roy Dr.
Doctoral Theses
There has been a peralstent empliasis both at the na tional and international levela on the developmont and application of techniques of estimation of demographio variablos from incomplete or inagcurute data in Coneietont wi th the theme of reuoaroh, the the lesu developed rogiona. present study tries to provide estimates of vital rates and prospective population trends in India and to form a basis for measuri.ng suoh hunan neede as vducation, employment, f'anily weltare,and few others in terms of population size,growth, ago s truature and nuptiality. The other major objectivu is to undertake furthor utilization of data generated by tihe …
Multisectoral Model Of Income Distribution Poverty And Growth:Some Policy Exercies For Indian Economy., Debdas Bandyopadhyay Dr.
Multisectoral Model Of Income Distribution Poverty And Growth:Some Policy Exercies For Indian Economy., Debdas Bandyopadhyay Dr.
Doctoral Theses
The extent of poverty in any country depends upon two factors vlz, the average level of income anxd the degree of inequality in its distribution. The central theme in the continuing debate on the relationship between growth and poverty is whether past growth process in the developing countries has caused any signi.licant benefit to the poor. Kuznets (1955) was first to observe from cross country data that procosa of development is likely to be accompanied by increase in inequality, whhich would reverse itself only at a relatively advanced stage. This hypothesis has been subsequently confirned to some extent by several …
Contributions To The Study Of Bayes Estimates: The Maximum Likelihood Estimate And Rao's Test., S. N. Joshi Dr.
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 …
Some Contributions To Bayes, Minimax And Admissible Decision Rules In One Parameter And Multiparameter Families., Anirban Das Gupta Dr.
Some Contributions To Bayes, Minimax And Admissible Decision Rules In One Parameter And Multiparameter Families., Anirban Das Gupta Dr.
Doctoral Theses
The study of admissible, minimax, and Bayes procedures has been of primary importance ever since the pioneering work of Wald (50). Since early seventies, new directions have been opening up, and not merely new techniques, completely new interpretations and interrelations have come to be known.To prove admissibility of estimates the most commonly used technique is to show that it is extended Bayes and approximate its risk by the risk of the corresponding Bayes estimates. This technique is due to Blyth (51). A sort of conver se result, which cssentially shows that this technique must work for all admissible est imates …
Optimal Strategies Under Superpopulation Models., V. R. Padmawar Dr.
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 …
Study Of The Robustness Of Inference Procedures In Linear Models With Specification Errors., Thomas Mathew Dr.
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).
On Specification And Statistical Inference In Single Equation Regression Models., Nityananda Sarkar Dr.
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 …
Estimation In Errors-In-Variables Models., Manoranjan Pal Dr.
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 …
Estimation Of A Common Mean And Recovery Of Inter Block Information., Chunni Gopal Bhattacharya Dr.
Estimation Of A Common Mean And Recovery Of Inter Block Information., Chunni Gopal Bhattacharya Dr.
Doctoral Theses
The problem of conbining several estimates of an unknown quentity to obtain an eetimete of Improved precieion arises in meny spheres of application of etatistics, To begin with let us consider the following simple inadelt1 =+4, 1- 1,...,kwhere u ie an unknown quantity and e, e ere errora with a common menn zero end a common veriance o. If we make no further asoumption about the distribution of e,s, the GAuas-Markoff theorem tells us that among sll unbtaved lineer combinationa ofr ya, the least squAre estimator i * Iy /k of u hes the minimum variance. If ,s are jointly …
Asymptotic Expansions And Deficiency., Tapas Kumar Chandra Dr.
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). …
Asymptotic Theory Of Extimation When The Limit Of The Log-Likelihood Ratios Is Mixed Normal., P. Jeganathan Dr.
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 …
Some Asymptotic Properties Of Maximum Likelihood Procedures., Kasala Subramaniam Dr.
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 …
Statistical Analysis Of Nonestimable Functionals., Dibyen Majumdar Dr.
Statistical Analysis Of Nonestimable Functionals., Dibyen Majumdar Dr.
Doctoral Theses
Our interent will be centred around the Gaunn Markov model (Y,X6,2A), where Y ls a randon variable asnuning values in R" with expectation and dispersion natrix given byE(Y) = XA (1.1) (1.2) * X in Rnxm and A In the subset of nonnegative definite (n.n.d.) natrices of RAre known. Unless apecifled to the contrary, A will be assuted to be positive definite (p.d.). The unknown paraneter vector B varies in Ag, a subset of Rand o? in, will alvays be the positive half of the real line, unless otherwine specifled, and 1ikewfse satiafien the minimum requirement dim (n,) = m.Historically, …
On Some Non Uniform Rates Of Convergence To Normality With Applications., Ratan Dasgupta Dr.
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 …
Some Problems On Econometric Regression Analysis., Maitreyi Chaudhuri Dr.
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 …