The global approach to nonlinear renewal theory is integrated with the author's own local approach. Both the theory and its applications are placed in perspective by including a discussion of the linear renewal theorem and its applications to the sequential probability ratio test. Applications to repeated significance tests, to tests with power one, and to sequential estimation are also included. The monograph is self-contained for readers with a working knowledge of measure-theoretic probability and intermediate statistical theory.

adjusted at the time of each breakdown.

An analogue of Blackwell's renewal theorem is obtained for processes Z sub n = S sub n + xi sub n, where S sub n is the nth partial sum of a sequence X1,X2, ... of independent identically distributed random variables with finite positive mean and xi sub n is independent of X sub n+1, X sub n+2,.. and has sample paths which are slowly changing in a sense made precise below. As a consequence, asymptotic expansions up to terms tending to 0 are obtained for the expected value of certain first passage times. Applications to sequential analysis are given.

Most of the research performed under this contract can be described under four broad, related categories: (1) Nonlinear renewal theory and its applications to sequential analysis; (2) corrected diffusion approximations and their applications; (3) sequential analysis of the proportional hazards model; and (4) change-point problems. Keywords: Bibliographies.

Sequential analysis refers to the body of statistical theory and methods where the sample size may depend in a random manner on the accumulating data. A formal theory in which optimal tests are derived for simple statistical hypotheses in such a framework was developed by Abraham Wald in the early 1

Sequential Analysis: Hypothesis Testing and Changepoint Detection systematically develops the theory of sequential hypothesis testing and quickest changepoint detection. It also describes important applications in which theoretical results can be used efficiently. The book reviews recent accomplishments in hypothesis testing and changepoint detection both in decision-theoretic (Bayesian) and non-decision-theoretic (non-Bayesian) contexts. The authors not only emphasize traditional binary hypotheses but also substantially more difficult multiple decision problems. They address scenarios with simple hypotheses and more realistic cases of two and finitely many composite hypotheses. The book primarily focuses on practical discrete-time models, with certain continuous-time models also examined when general results can be obtained very similarly in both cases. It treats both conventional i.i.d. and general non-i.i.d. stochastic models in detail, including Markov, hidden Markov, state-space, regression, and autoregression models. Rigorous proofs are given for the most important results. Written by leading authorities in the field, this book covers the theoretical developments and applications of sequential hypothesis testing and sequential quickest changepoint detection in a wide range of engineering and environmental domains. It explains how the theoretical aspects influence the hypothesis testing and changepoint detection problems as well as the design of algorithms.

Sequential Analysis: Hypothesis Testing and Changepoint Detection systematically develops the theory of sequential hypothesis testing and quickest changepoint detection. It also describes important applications in which theoretical results can be used efficiently. The book reviews recent accomplishments in hypothesis testing and changepoint detecti