- e SEQUENTIAL AND TIME - SEQUENTIAL PROCEDURES FOR GENERALIZED MODELS

In statistical inference it is often desired to test a specified function of unknown parameters from an underlying distribution. Sequential procedures utilize information from the already collected observations and allow for a possible early termination of experimentation with a concurrent savings in time and cost. They also enable the investigator to prescribe bounds for both the Type I and Type II errors and therefore are preferred to fixed sample testing procedures when their implementation is possible from a practical standpoint. In the present work we develop suitable sequential testing procedures for functions of unknown parameters through extensions of results by Bartlett (1946) and Chatterjee and Sen (1973). In the case when the form of the underlying distributions is kno~~, the use of maximum likelihood techniques allows development of a suitable sequential test for a broad class of specified functions of interest for i.i.d. as well as time-dependent observations. The test procedure is based on a generalization of the Sequential Likelihood Ratio Test (SLRT) proposed by Bartlett (1946) and Cox (1963). Theoretical justification for the generalization of the SLRT suggested by Cox (1963) is provided. The theoretical Operating Characteristic (OC) and Average Sample Number (ASN) functions are derived for local alternatives by approximating the distribution of the test statistic with linear combinations of standard Brownian Motion processes for both the i.i.d. and time-dependent observation cases. Simulation studies were utilized to investigate the goodness of the asymptotic results in finite samples. It is shown that the two-sample comparison testing iii problem is a special case of our general sequential testing framework. When the form of the underlying distribution is unknown, robust sequential tests based on suitable rank order statistics were developed for testing a function of multiple regression parameters for i.i.d. observations. The DC and ASN functions of the sequential test are examined under local alternatives. The problem of rank order estimation of unknown mUltiple regression parameters for time-dependent observations in a Progressively Censored Scheme (PCS) is discussed. The possible implementation of the proposed sequential testing procedure in compliance testing for air pollution monitoring is studied as an example. Some of the numerous applications of the sequential testing procedures are presented. iv ACKNOWLEDGMENTS It has been a very special priviledge during this research to work for their helpful suggestions and ideas which went into this dissertation. In addition, I wish to thank my parents Pushpa and Ishver Bangdiwala as well as my …