Nonlinear Renewal Theory in Sequential Analysis (CBMS-NSF Regional Conference Series in Applied Mathematics) (CBMS-NSF Regional Conference Series in Applied Mathematics)

Annotation 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 Nonlinear Renewal Theory in Sequential Analysis......Page 3 ISBN: 0-89871-180-0......Page 4 Contents......Page 5 Preface......Page 7 Introduction......Page 9 1 Randomly Stopped Sequences......Page 11 2 Random Walks......Page 23 3 The Sequential Probability Ratio Test......Page 37 4 Nonlinear Renewal Theory......Page 49 5 Local Limit Theorems......Page 61 6 Open-ended Tests......Page 69 7 Repeated Significance Tests......Page 79 8 Multiparameter Problems......Page 97 9 Estimation Following Sequential Testing......Page 107 10 Sequential Estimation......Page 113 Appendix: Proof of the Renewal Theorem......Page 121 References......Page 125