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Full-Text Articles in Physical Sciences and Mathematics
Statistical Analysis Of Economic Activities For Developement In Nepal., Bishnu Pant Dr.
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 …
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 …
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).