Physical Sciences and Mathematics Commons^™

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.

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 …

Student Profile, Fall 1982, Division Of Student Affairs, Wright State University, Dayton, Ohio, Office Of Student Information Systems, Wright State University

Wright State University Student Fact Books

The student profile fact book has general demographic information on all students enrolled at Wright State University for Fall Quarter, 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 …

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.

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 …

Climate Data Sources In Connecticut, Patricia A. Palley, David R. Miller

Storrs Agricultural Experiment Station

No abstract provided.

Some Comments On The Erdos-Renyl Law And A Theorem Of Shepp, James Lynch

Faculty Publications

We show that the finiteness of the moment generating function is necessary for the finiteness of the lim sup of the moving averages considered by Shepp (1964). This also implies that the same must be true for the Erdos-Renyi law of large numbers.

Student Profile, Fall 1981, Wright State University, Dayton, Ohio, Office Of Student Information Systems, Wright State University

Wright State University Student Fact Books

The student profile fact book has general demographic information on all students enrolled at Wright State University for Fall Quarter, 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). …

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 …

Student Profile, Fall 1980, Wright State University, Dayton, Ohio, Office Of Student Information Systems, Wright State University

Wright State University Student Fact Books

The student profile fact book has general demographic information on all students enrolled at Wright State University for Fall Quarter, 1980. The cover of the book has a 1980 sticker on it as well as an ink stamp that reads, "Wright State University Student Information Systems".

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.

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.

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.

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 …

Student Profile, Fall 1979, Wright State University, Dayton, Ohio, Office Of Student Information Systems, Wright State University

Wright State University Student Fact Books

The student profile fact book has general demographic information on all students enrolled at Wright State University for Fall Quarter, 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 …

The Prior Distribution In Bayesian Statistics, Kai-Tang Chen

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

A major problem associated with Bayesian estimation is selecting the prior distribution. The more recent literature on the selection of the prior is reviewed. Very little of a general nature on the selection of the prior is formed in the literature except for non-informative priors. This class of priors is seen to have limited usefulness. A method of selecting an informative prior is generalized in this thesis to include estimation of several parameters using a multivariate prior distribution. The concepts required for quantifying prior information is based on intuitive principles. In this way, it can be understood and controlled by …

Theory Of Estimation In Algebraic And Analytic Exponential Families With Applications To Variance Components Models., Krishnan Unni Dr.

Doctoral Theses

There are many important statistical problems of the following kind. The family of probability measures O is parametrized by a vector parame ter n varying in a q-dimen- sional domain. P can be represented as an exponential family of probability distributions with k canonical para- me ters where k is greater than q. The canonical parameters do not vary in a domain in R, but are restricted by polyno- mial or analytic equations. They vary on a curved surface defined by the polynomial or analytic equations within the natural parame ter space of the exponential family. The present work is …

Student Profile, Fall 1978, Wright State University, Dayton, Ohio, Office Of Student Information Systems, Wright State University

Wright State University Student Fact Books

The student profile fact book has general demographic information on all students enrolled at Wright State University for Fall Quarter, 1978.

The Maine Coast, A Statistical Source, Maine Coastal Program

Maine Collection

The Maine Coast, A Statistical Source

Maine Coastal Program, Natural Resource Planning Division, Maine State Planning Office , Augusta, Maine

First Printing June 1978 - Second Printing September 1978

Contents: Preface / Introduction / Chapter 1 - Demography / Chapter 2 - Land Use and Taxation / Chapter 3 - Economy / Chapter 4 - Housing / Chapter 5 - Transportation / Chapter 6 - Education / Chapter 7 - Recreation / Chapter 8 - Social Services / Chapter 9 - Natural Resources / References / Index

Student Profile, Fall 1977, Wright State University, Dayton, Ohio, Office Of Student Information Systems, Wright State University

Wright State University Student Fact Books

The student profile fact book has general demographic information on all students enrolled at Wright State University for Fall Quarter, 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 …

Sequential Methods In Estimation And Prediction., Nitis Mukhopadhyay Dr.

Doctoral Theses

No abstract provided.

Price, Income, Interest In A Two Sector Model Of Agriculture And Non-Agriculture: A Theoretical And Empirical Analysis For Indian Economy., Pradip Maiti Dr.

Doctoral Theses

A macroeconometric model seeks to portray the functioning of an economy at an aggregative level, i.e., in terms of important macrovariables and their interrelationships. The empirical counterpart of such a model is what is called a macroeconometric model when the macrorelations are posited statistically, employing probabilistic methods of estimation and/or hypothesis testing. The present study covers both aspects of a macromodel. On the theoretical side, it builds up a macroeconomic model which may be relevant for a country like India. On the empirical-statistical side, it goes on to formulate a macroeconometric model. There is a clear interdependence between these two …

Contributions To The Theory Of Optimum Utilisation Of Auxiliary Information In Survey Sampling., V. N. Reddy Dr.

Doctoral Theses

The main problem of Survey sapling fron finite populations consista of devistng an appropriate procodure for solecting a rapresentative srple frøn a glven popalation and dornloping an apprepriate procedure for the estimation of the population parceeter of interest guch as po pulation nean or total or population ratto with a viev to naxinising the preofsion of the estinstor vithin the available resources of tino and ooat or 6iternati vely minimising the aost for achieving a giren level of prestsion, Towards the solution of this problen 1t is only during the thirties ond forties that a nore systematie develop- nant has …

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, …

On A General Class Of Unbiased Ratio, Product, Ratio-Cum-Product And Regression Type Estimators., N. S. Sastry Dr.

Doctoral Theses

Probability enmpling methods ha ve extenaive a pplication in la rge- eca le agricultural and socio economic surve ys, Sampling is ale used in one or more stages of a census and sometimes as a mubstitute for a complete Census. Over the pa st four deca de s, confidence in the use of san pling and a ppreciation for the technique have stee dily grown thanks to the pi onee ring efforts of Neyman, Hansen, Hurwit z, Maha lanobis, Sukha tme, Cochran, Yate s and others.2. It is well known that the principa i problem of the theory of sampling …

Computer Programs Supporting The Teaching Of Statistics, Chien-Hwa Liu

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

During the past few years there has been an increasing interest in developing computer packages to enhance the teaching of elementary statistics. The conventional ways of teaching statistics have used such devices as desk calculators, tables of functions, short-cut calculating formulas and electronic calculators, etc. to manipulate the involved computations. Electronic computers, in the past decade, have been broadly used in universities and colleges in many ways. It is only natural to extend the use of computers to the teaching function. Remote terminals can now be installed in any classroom and bring the computer to the students.