Date of Submission


Date of Award


Institute Name (Publisher)

Indian Statistical Institute

Document Type

Doctoral Thesis

Degree Name

Doctor of Philosophy

Subject Name



Theoretical Statistics and Mathematics Unit (TSMU-Kolkata)


Ghosh, Jayanta Kumar (TSMU-Kolkata; ISI)

Abstract (Summary of the Work)

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). The latter paper, together with some spplications to maltivariata testing problens discussed in Chandra and hosh (1980b), forms Part II of this disseration. Part I is & study of valid asymptotie expans ions for test statistics which inolude the 1ikelihood ratio criterion, Walds and Rans statis- ties (see Rao (1965) s pagos 347-352). These statistics have the Juna liniting Ä‘istribution under the null hypothesis as wall as under contiguous alternatives hence they have the same Pitman effieiency. The above-mentioned asymptotic expansions are needed to atudy the Pitnan-da fieieney of these procedures relat ive to eadh other.Since a subatant Lal part of this thests la onneernad vith Bahadur orrie ioney, it Is impossible to ignore the eritieism of Bahadur's aaymptoties by LaCan (1974) (see pages 232 and 233) as a study of ghosta of departed quantities i this reitark has been quoted vith approval by Pfanz agl (1980) (sea page 27, Sect lon 3.3e). o doubt there is sone truth in this eritietan but It applies e qually well to all other asyuptotie theorles. Only the Ghosts Appear at difrerent places in dirferent theories. In the asyipto- tles of Pitaman (and LeCan, Pfanzagl and others), the "distance" between the null hypothesis .oo and on altornative zero and so after a finitely many/steps the dirrerence betwaen oo goes to on. and beconea "practically" irrelevant; why ahould one then be interested in distinguishing such (elose) hypothases Jal aymptoties are no more than an approxinat ion to the rinite problen of real lire. One can only hope that the ghosts provide a clue (?) to the soul ir not the body of ones actual problem.


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