Date of Submission


Date of Award


Institute Name (Publisher)

Indian Statistical Institute

Document Type

Doctoral Thesis

Degree Name

Doctor of Philosophy

Subject Name

Computer Science


Theoretical Statistics and Mathematics Unit (TSMU-Kolkata)


Ghosh, Jayanta Kumar (TSMU-Kolkata; ISI)

Abstract (Summary of the Work)

The area of sequential testing of statistical hypothesss is an important part of sequential analysis. The idea of a sequential test goes back to Dodge and Romig (1929) who cons tructed a double sampling procedure for sampling inspection. They wers motivated by the obser- vation that the double sampling plan requires a smaller number of observations on the average when compared uith the corresponding single sampling plan, Later schemes like multiple sampling vide Wlalter Bartky (1943) and interesting practical application of large scale experimente in successive stages vide Mahalanobis (1940) started comni ng up.The formal theory in sequential analysis began in about 1943 with the work of A. Wald in America (vide Wald (1945)) and G.A. Barnard (vide Barnard (1946)) in Britain in war time industrial advisory graups. The discovery of walds sequential probability ratio test (SPRT) was consider ed to be most important. An elegant theory of SPRT is given in Wald (1947) and a review with a list of references can be found in Johnson (1961). 8arnerd (1947) also gives a review of wald (1947).The subject of sequential analysis has undergone a rapid develop- ment since the formal theory came up. For some nore references in this area one may look into Watherill (1965) and Ghosh (1970).This thesis deals with the problem of testing of hypotheses, sequentially, arising from identification and selection probleme It also gives a numerical solution to a free boundery problom (f. b. p.) arising from the problem of testing sequentially the sign of the drift parameter of a wiener process.The problem of identification or classification of an individual into one of the two categories is well known in statistical literature. If the two categories are completely specified then one can adopt a sequential test with an aim to control the errors of misclassification. This has been done by Rao (1948), Armitage (1950) and Mallows (1953). Soquential techniques are adopted even when the categories are partially specified vide Srivastava (1973) and Chosh and Mukhopadhyay (1980). A more deteiled discussion of these works can be found in Section 2.1 of Chapter 2.Selection and ranking of populations is another important erea of Statistics. A vast litereture is available in this area. Tho sequentíal methods for selection and ranking are summarised beautifully by Bechhofer, Kiefer and Sobel (1968). Both sequential and.non-eequential methodo usef ul for selection and ranking problems can bo found in Gupta and Panchapakeshan (1979) as well as in Gibbons, 0lkin and Sobel (1977).The problem of solecting one population (bost or worst in some well defined sense) out of k-many populations (k 2 2) is most common in selaction problems. If the populations are reasonably specified then once agein sequential procedures can be adopted with a target of reaching the prespecifiad probability of correct selection namely p* The idea of sequential procedutes of choosing one out of k-many hypothes es using likelihoods goes back to Wald (1947, Chapter 10 and subsequently by Sobel and Wald (1949), Armitage (1950), Meili json (1969), Hoel (1971), Robbins (1970), Khan (1973) and recently by Mukhopadhyay (1983).


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