Date of Submission


Date of Award


Institute Name (Publisher)

Indian Statistical Institute

Document Type

Doctoral Thesis

Degree Name

Doctor of Philosophy

Subject Name



Research and Training School (RTS)


Bahadur, Raghu Raj (RTS-Kolkata; ISI)

Abstract (Summary of the Work)

This thesis is being submitted to the Indian statistical Institute in support of the author's application for the degree of doctor of philosophy. The thesis embodies research carried out by the author during the period 1958-1961 under the supervision of dr.R.R. Bahadur, Professor of statistics are the Indian Statistical Institute Calcutta.This thesis is concerned with development of a new method of establishing asymptotic distributions and the elaboration of some of its applications in several fields of statistics.The thesis consists of five chapters. Chapter I describes, in general terms, the various problems considered in the thesis. Chapter II Deals with the basic results concerning the convergence of joint distributions under assumptions about the convergence of marginal and conditional distributions. Chapter III is devoted to the applications of the result of chapter II to some problems in in statistical methods. Chapter IV and V deal with some applications to Regression Analysis. Chapter V also contains the results of some model sampling experiments, and tables for practical use.Earlier versions of some of the results of Chapter III have appeared as joint article with Dr. B. V. Sukhatme of the Indian Council of Agricultural Research, New Delhi, in Sankhya, 21 (1959) 289-298 (Ref. 49 ]). Some of the results of Chapter IV have appeared in Sankhya, Series ,A, 23(1961), 73-90. (Ref. ( 48 1.)The author wishes to express his sincere gratitude to Dr. R.R, Bahadur for his guidance and advice on the method of presentation of the material in the thesis, and to Dr. C. R. Rao, Professor and Head of the Division of Theoretical Research and Training, Indian Statistical Institute, for his constant encouragement. The author is indebted to the following members of the Indian Statistical Institute:to Sri Nikilesh Bhattacharya for his help in some modol sampling experiments and for his reading Chapters IN and V; to Sri G. Parthas are thy for his help in some model sampling experinents; and so Sri T. Krishnamurthi and to Sri Debdas Choudhuri for theircom putation of tables I, II, III and IV on the electronic computer. The author also wishes to express his gratitude to Sri K.R.parthasarathy of the Indian Statis tical Institute for procuring and translating N.V. Smirnovs article (Ref. [ 50 ], which necessitated a revision of an earlier version of Chapter III.The author also records his gratefulness to the Research and The Training School of Indian Statistical Institute for providing facilities for research. Thanks are due to Sri G.M. Das for his efficient typing of the Thesis.


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