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Recent Advances in Statistics : Papers in Honor of Herman Chernoff on His Sixtieth Birthday.

By: Rizvi, M. HaseebContributor(s): Rustagi, Jagdish S | Siegmund, DavidMaterial type: TextTextSeries: eBooks on DemandPublisher: Kent : Elsevier Science & Technology, 2014Copyright date: ©1983Description: 1 online resource (626 pages)Content type: text Media type: computer Carrier type: online resourceISBN: 9781483266602Subject(s): Chernoff, Herman | Mathematical statistics | Mathematicians -- United States -- BiographyGenre/Form: Electronic books.Additional physical formats: Print version:: Recent Advances in Statistics : Papers in Honor of Herman Chernoff on His Sixtieth BirthdayDDC classification: 519.5 LOC classification: QA276.16.R43 1983Online resources: Click here to view this ebook.
Contents:
Front Cover -- Recent Advances in Statistics: Papers in Honor of Herman Chernoff on His Sixtieth Birthday -- Copyright Page -- Table of Contents -- CONTRIBUTORS -- PREFACE -- HERMAN CHERNOFF: AN APPRECIATION -- PUBLICATIONS OF HERMAN CHERNOFF -- PART I: SEQUENTIAL ANALYSIS INCLUDING DESIGNS -- CHAPTER 1. OPTIMAL STOPPING OF BROWNIAN MOTION: A COMPARISON TECHNIQUE -- I. INTRODUCTION AND SUMMARY -- II. STOPPING PROBLEMS FOR BROWNIAN MOTION -- III. BANDIT PROBLEMS -- IV. GITTINS INDICES FOR NORMAL PROCESSES -- V. THE BUYER'S PROBLEM -- VI. REFERENCES -- CHAPTER 2. SEQUENTIAL DESIGN OF COMPARATIVE CLINICAL TRIALS -- I. INTRODUCTION -- II. THE CONTINUOUS-TIME PROBLEM AND A CLASS OF STOPPING RULES -- III. ASYMPTOTIC OPTIMALITY OF THE CLASS C OF STOPPING BOUNDARIES -- IV. SOME ASYMPTOTICALLY SUBOPTIMAL STOPPING RULES -- V. REFERENCES -- CHAPTER 3. THE CRAMÉR-RAO INEQUALITY HOLDS ALMOST EVERYWHERE -- I. INTRODUCTION -- II. THE FIXED SAMPLE SIZE CASE -- III. THE SEQUENTIAL CASE -- IV. REMARKS -- V. ACKNOWLEDGMENTS -- VI. APPENDIX A -- VII. APPENDIX B -- VIII. REFERENCES -- CHAPTER 4. A TWO-SAMPLE SEQUENTIAL TEST FOR SHIFT WITH ONE SAMPLE SIZE FIXED IN ADVANCE -- I. INTRODUCTION -- II. PROBLEM SPECIFICATION AND THE SUGGESTED PROCEDURE -- III. CALCULATION OF ERROR PROBABILITIES -- IV. AVERAGE NEW DATA SAMPLE-SIZE -- V. COMPARISON WITH A FIXED NUMBER OF NEW DATA OBSERVATIONS -- VI. OPTIMIZATION OF THE SEQUENTIAL PROCEDURE WHEN THE "OLD" DATA IS STILL TO BE COLLECTED -- COMPARISON WITH BEST FIXED SAMPLE-SIZE PROCEDURES AND PROCEDURES FOR SAMPLING IN PAIRS -- VII. APPENDIX -- VIII. REFERENCES -- CHAPTER 5. ON SEQUENTIAL RANK TESTS -- I. INTRODUCTION -- II. PRELIMINARIES -- III. THE MAIN THEOREM -- IV. A SEQUENTIAL PROBABILITY RATIO TEST -- V. REFERENCES -- PART II: OPTIMIZATION INCLUDING CONTROL THEORY.
CHAPTER 6. A NON-HOMOGENEOUS MARKOV MODEL OF A CHAIN-LETTER SCHEME -- I. INTRODUCTION -- II. A MARKOV MODEL OF THE RECRUITMENT PROCESS AND ITS DIFFUSION APPROXIMATION -- III. TERMINATION OF THE RECRUITMENT PROCESS -- IV. A BOUND FOR THE SIZE OF THE SUB-CHAIN STARTED BY THE kth PARTICIPANT -- V. MONTE CARLO SIMULATION OF THE PROCESS -- VI. ACKNOWLEDGMENT -- REFERENCES -- CHAPTER 7. SET-VALUED PARAMETERS AND SET-VALUED STATISTICS -- I. INTRODUCTION -- II. PRELIMINARIES -- III. SUFFICIENCY -- IV. MAXIMUM LIKELIHOOD ESTIMATORS -- V. BAYESIAN METHODS -- VI. EXAMPLES -- REFERENCES -- CHAPTER 8. OPTIMAL SEQUENTIAL DECISIONS IN PROBLEMS INVOLVING MORE THAN ONE DECISION MAKER -- I. INTRODUCTION -- II. A SIMPLE GAME -- III. THE STOCHASTIC GAME -- IV. A MORE GENERAL GAME -- V. DISCUSSION -- VI. REFERENCES -- CHAPTER 9. AN AVERAGING METHOD FOR STOCHASTIC APPROXIMATIONS WITH DISCONTINUOUS DYNAMICS, CONSTRAINTS, AND STATE DEPENDENT NOISE -- I. INTRODUCTION -- III. THE PROJECTION METHOD -- IV. STATE DEPENDENT NOISE -- V. EXAMPLES -- REFERENCES -- CHAPTER 10. ENLIGHTENED APPROXIMATIONS IN OPTIMAL STOPPING -- I. CHARACTERISATIONS -- II. THE MAXIMISATION OF A SAMPLE MEAN -- III. EVALUATION OF THE GITTINS INDEX -- IV. REFERENCES -- CHAPTER 11. SURVEY OF CLASSICAL AND BAYESIAN APPROACHES TO THE CHANGE-POINT PROBLEM: FIXED SAMPLE AND SEQUENTIAL PROCEDURES OF TESTING AND ESTIMATION -- I. INTRODUCTION -- II. TESTING HYPOTHESES CONCERNING CHANGE POINTS -- III. ESTIMATING THE LOCATION OF THE SHIFT POINT -- IV. DYNAMIC CONTROL PROCEDURES -- REFERENCES -- PART III: NONPARAMETRICS INCLUDING LARGE SAMPLE THEORY -- CHAPTER 12. LARGE DEVIATIONS OF THE MAXIMUM LIKELIHOOD ESTIMATE IN THE MARKOV CHAIN CASE -- I. INTRODUCTION -- II. PROOF -- REFERENCES -- CHAPTER 13. BAYESIAN DENSITY ESTIMATION BY MIXTURES OF NORMAL DISTRIBUTIONS -- I. INTRODUCTION -- II. THE PRIOR.
III. CONNECTION WITH THE DIRICHLET PROCESS -- IV. COMPUTATIONS -- V. IMPROVING THE MONTE CARLO -- VI. SUMMARY -- REFERENCES -- CHAPTER 14. AN EXTENSION OF A THEOREM OF H. CHERNOFF AND E. L. LEHMANN -- I. INTRODUCTION -- II. TEST CRITERIA FOR THE GAUSSIAN CASE -- III. GAUSSIAN THEORY UNDER THE NULL HYPOTHESIS -- IV. ASYMPTOTICS UNDER THE NULL HYPOTHESIS -- V. ASYMPTOTIC BEHAVIOR UNDER ALTERNATIVES -- VI. REFERENCES -- CHAPTER 15. THE LIMITING BEHAVIOR OF MULTIPLE ROOTS OF THE LIKELIHOOD EQUATION -- I. INTRODUCTION -- II. NOTATION AND PRELIMINARY LEMMAS -- III. GLOBAL LIMITING BEHAVIOR OF Sn -- IV. LOCAL LIMITING BEHAVIOR OF Sn -- V. SOME EXAMPLES OF K-L ORDERED FAMILIES -- VI. TWO SPECIAL FAMILIES -- VII. IMPLICATIONS FOR THE ESTIMATION OF θ0 -- VIII. CONCLUDING REMARKS -- REFERENCES -- CHAPTER 16. ON SOME RECURSIVE RESIDUAL RANK TESTS FOR CHANGE-POINTS -- I. INTRODUCTION -- II. RECURSIVE RESIDUAL RANK TESTS FOR THE LOCATION MODEL -- III. RECURSIVE RESIDUAL RANK TESTS FOR THE REGRESSION MODEL -- IV. ASYMPTOTIC PROPERTIES OF Dn+ AND Dn -- V. ASYMPTOTIC RELATIVE EFFICIENCY RESULTS -- VI. APPENDIX -- VII. ACKNOWLEDGMENT -- VIII. REFERENCES -- CHAPTER 17. OPTIMAL UNIFORM RATE OF CONVERGENCE FOR NONPARAMETRIC ESTIMATORS OF A DENSITY FUNCTION OR ITS DERIVATIVES -- I. INTRODUCTION -- II. PROOF OF THEOREM 2 -- REFERENCES -- CHAPTER 18. RANKS AND ORDER STATISTICS -- I. INTRODUCTION -- II. THE RESULT -- III. PROOF -- IV. APPENDIX -- V. REFERENCES -- PART IV: STATISTICAL GRAPHICS -- CHAPTER 19. M AND N PLOTS -- I. INTRODUCTION -- II. EXAMPLES OF M AND N PLOTS -- III. SOME PRACTICAL DETAILS -- IV. ACKNOWLEDGMENT -- V. REFERENCES -- CHAPTER 20. INVESTIGATING THE SPACE OF CHERNOFF FACES -- I. AN EMPIRICAL METHOD FOR EVALUATING REGIONS OF THE SPACE OF FACE PARAMETER VECTORS -- II. AN EMPIRICAL METHOD FOR ASSIGNING COORDINATES TO FACIAL FEATURES -- III. CONCLUSIONS.
ACKNOWLEDGMENTS -- REFERENCES -- CHAPTER 21. ON MULTIVARIATE DISPLAY -- Tables -- Inside-Out Plots -- Function Plots -- Polygons -- Trees -- Faces -- Extensions -- Conclusions -- Seeing vs. Reading a Display -- An Appreciation -- Acknowledgments -- References -- PART V: OTHER TOPICS -- CHAPTER 22. MINIMAX ESTIMATION OF THE MEAN OF A NORMAL DISTRIBUTION SUBJECT TO DOING WELL AT A POINT -- SUMMARY -- I. THE PROBLEM -- II. OPTIMAL AND SUBOPTIMAL PROCEDURES AND THE CONNECTION TO ROBUST ESTIMATION OF LOCATION -- III. THE BEHAVIOUR OF μ (t) FOR SMALL t -- IV. THE BEHAVIOUR OF μ (t) FOR t CLOSE TO 1 -- V. ACKNOWLEDGMENT -- VI. REFERENCES -- CHAPTER 23. SOME NEW DICHOTOMOUS REGRESSION METHODS -- I. INTRODUCTION -- II. MODELS FOR PREDICTING THE OUTCOME OF INTENSIVE CARE -- III. ANALOGIES TO NORMAL REGRESSION AND R2 -- IV. A SCREENING PROCEDURE FOR GOODNESS OF FIT -- V. EXAMINATION OF THE LIKELIHOOD SURFACE -- VI. DISCUSSION AND CONCLUSION -- ACKNOWLEDGMENT -- REFERENCES -- CHAPTER 24. THE APPLICATION OF SPLINE FUNCTIONS TO THE PHARMACOKINETIC ANALYSIS OF METHOTREXATE INFUSED INTO MALIGNANT EFFUSIONS -- I. INTRODUCTION -- II. ANALYSIS AND RESULTS -- III. DISCUSSION -- IV. ACKNOWLEDGMENTS -- V. REFERENCES -- CHAPTER 25. SELECTING REPRESENTATIVE POINTS IN NORMAL POPULATIONS -- REFERENCES -- CHAPTER 26. LEAST INFORMATIVE DISTRIBUTIONS -- I. INTRODUCTION -- II. THE NORMAL DISTRIBUTION -- III. THE CASE n = 2 -- IV. EXPONENTIAL DISTRIBUTION -- V. A MINIMAX FORMULATION -- VI. REFERENCES -- CHAPTER 27. SIGNIFICANCE LEVELS, CONFIDENCE LEVELS, CLOSED REGIONS, CLOSED MODELS, AND DISCRETE DISTRIBUTIONS -- I. INTRODUCTION -- II. TESTS -- III. CONFIDENCE PROCEDURES -- IV. REMARKS -- REFERENCES.
Summary: Recent Advances in Statistics: Papers in Honor of Herman Chernoff on His Sixtieth Birthday is a collection of papers on statistics in honor of Herman Chernoff on the occasion of his 60th birthday. Topics covered range from sequential analysis (including designs) to optimization (including control theory), nonparametrics (including large sample theory), and statistical graphics. Comprised of 27 chapters, this book begins with a discussion on optimal stopping of Brownian motion, followed by an analysis of sequential design of comparative clinical trials. A two-sample sequential test for shift with one sample size fixed in advance is then presented. Subsequent chapters focus on set-valued parameters and set-valued statistics; large deviations of the maximum likelihood estimate in the Markov chain case; the limiting behavior of multiple roots of the likelihood equation; and optimal uniform rate of convergence for nonparametric estimators of a density function and its derivatives. The book concludes by considering significance and confidence levels, closed regions and models, and discrete distributions. This monograph should be of interest to students, researchers, and specialists in the fields of mathematics and statistics.
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Electronic Book UT Tyler Online
Online 		QA276.16 -- .R43 1983 (Browse shelf) http://ebookcentral.proquest.com/lib/uttyler/detail.action?docID=1901764 Available EBC1901764

Front Cover -- Recent Advances in Statistics: Papers in Honor of Herman Chernoff on His Sixtieth Birthday -- Copyright Page -- Table of Contents -- CONTRIBUTORS -- PREFACE -- HERMAN CHERNOFF: AN APPRECIATION -- PUBLICATIONS OF HERMAN CHERNOFF -- PART I: SEQUENTIAL ANALYSIS INCLUDING DESIGNS -- CHAPTER 1. OPTIMAL STOPPING OF BROWNIAN MOTION: A COMPARISON TECHNIQUE -- I. INTRODUCTION AND SUMMARY -- II. STOPPING PROBLEMS FOR BROWNIAN MOTION -- III. BANDIT PROBLEMS -- IV. GITTINS INDICES FOR NORMAL PROCESSES -- V. THE BUYER'S PROBLEM -- VI. REFERENCES -- CHAPTER 2. SEQUENTIAL DESIGN OF COMPARATIVE CLINICAL TRIALS -- I. INTRODUCTION -- II. THE CONTINUOUS-TIME PROBLEM AND A CLASS OF STOPPING RULES -- III. ASYMPTOTIC OPTIMALITY OF THE CLASS C OF STOPPING BOUNDARIES -- IV. SOME ASYMPTOTICALLY SUBOPTIMAL STOPPING RULES -- V. REFERENCES -- CHAPTER 3. THE CRAMÉR-RAO INEQUALITY HOLDS ALMOST EVERYWHERE -- I. INTRODUCTION -- II. THE FIXED SAMPLE SIZE CASE -- III. THE SEQUENTIAL CASE -- IV. REMARKS -- V. ACKNOWLEDGMENTS -- VI. APPENDIX A -- VII. APPENDIX B -- VIII. REFERENCES -- CHAPTER 4. A TWO-SAMPLE SEQUENTIAL TEST FOR SHIFT WITH ONE SAMPLE SIZE FIXED IN ADVANCE -- I. INTRODUCTION -- II. PROBLEM SPECIFICATION AND THE SUGGESTED PROCEDURE -- III. CALCULATION OF ERROR PROBABILITIES -- IV. AVERAGE NEW DATA SAMPLE-SIZE -- V. COMPARISON WITH A FIXED NUMBER OF NEW DATA OBSERVATIONS -- VI. OPTIMIZATION OF THE SEQUENTIAL PROCEDURE WHEN THE "OLD" DATA IS STILL TO BE COLLECTED -- COMPARISON WITH BEST FIXED SAMPLE-SIZE PROCEDURES AND PROCEDURES FOR SAMPLING IN PAIRS -- VII. APPENDIX -- VIII. REFERENCES -- CHAPTER 5. ON SEQUENTIAL RANK TESTS -- I. INTRODUCTION -- II. PRELIMINARIES -- III. THE MAIN THEOREM -- IV. A SEQUENTIAL PROBABILITY RATIO TEST -- V. REFERENCES -- PART II: OPTIMIZATION INCLUDING CONTROL THEORY.

CHAPTER 6. A NON-HOMOGENEOUS MARKOV MODEL OF A CHAIN-LETTER SCHEME -- I. INTRODUCTION -- II. A MARKOV MODEL OF THE RECRUITMENT PROCESS AND ITS DIFFUSION APPROXIMATION -- III. TERMINATION OF THE RECRUITMENT PROCESS -- IV. A BOUND FOR THE SIZE OF THE SUB-CHAIN STARTED BY THE kth PARTICIPANT -- V. MONTE CARLO SIMULATION OF THE PROCESS -- VI. ACKNOWLEDGMENT -- REFERENCES -- CHAPTER 7. SET-VALUED PARAMETERS AND SET-VALUED STATISTICS -- I. INTRODUCTION -- II. PRELIMINARIES -- III. SUFFICIENCY -- IV. MAXIMUM LIKELIHOOD ESTIMATORS -- V. BAYESIAN METHODS -- VI. EXAMPLES -- REFERENCES -- CHAPTER 8. OPTIMAL SEQUENTIAL DECISIONS IN PROBLEMS INVOLVING MORE THAN ONE DECISION MAKER -- I. INTRODUCTION -- II. A SIMPLE GAME -- III. THE STOCHASTIC GAME -- IV. A MORE GENERAL GAME -- V. DISCUSSION -- VI. REFERENCES -- CHAPTER 9. AN AVERAGING METHOD FOR STOCHASTIC APPROXIMATIONS WITH DISCONTINUOUS DYNAMICS, CONSTRAINTS, AND STATE DEPENDENT NOISE -- I. INTRODUCTION -- III. THE PROJECTION METHOD -- IV. STATE DEPENDENT NOISE -- V. EXAMPLES -- REFERENCES -- CHAPTER 10. ENLIGHTENED APPROXIMATIONS IN OPTIMAL STOPPING -- I. CHARACTERISATIONS -- II. THE MAXIMISATION OF A SAMPLE MEAN -- III. EVALUATION OF THE GITTINS INDEX -- IV. REFERENCES -- CHAPTER 11. SURVEY OF CLASSICAL AND BAYESIAN APPROACHES TO THE CHANGE-POINT PROBLEM: FIXED SAMPLE AND SEQUENTIAL PROCEDURES OF TESTING AND ESTIMATION -- I. INTRODUCTION -- II. TESTING HYPOTHESES CONCERNING CHANGE POINTS -- III. ESTIMATING THE LOCATION OF THE SHIFT POINT -- IV. DYNAMIC CONTROL PROCEDURES -- REFERENCES -- PART III: NONPARAMETRICS INCLUDING LARGE SAMPLE THEORY -- CHAPTER 12. LARGE DEVIATIONS OF THE MAXIMUM LIKELIHOOD ESTIMATE IN THE MARKOV CHAIN CASE -- I. INTRODUCTION -- II. PROOF -- REFERENCES -- CHAPTER 13. BAYESIAN DENSITY ESTIMATION BY MIXTURES OF NORMAL DISTRIBUTIONS -- I. INTRODUCTION -- II. THE PRIOR.

III. CONNECTION WITH THE DIRICHLET PROCESS -- IV. COMPUTATIONS -- V. IMPROVING THE MONTE CARLO -- VI. SUMMARY -- REFERENCES -- CHAPTER 14. AN EXTENSION OF A THEOREM OF H. CHERNOFF AND E. L. LEHMANN -- I. INTRODUCTION -- II. TEST CRITERIA FOR THE GAUSSIAN CASE -- III. GAUSSIAN THEORY UNDER THE NULL HYPOTHESIS -- IV. ASYMPTOTICS UNDER THE NULL HYPOTHESIS -- V. ASYMPTOTIC BEHAVIOR UNDER ALTERNATIVES -- VI. REFERENCES -- CHAPTER 15. THE LIMITING BEHAVIOR OF MULTIPLE ROOTS OF THE LIKELIHOOD EQUATION -- I. INTRODUCTION -- II. NOTATION AND PRELIMINARY LEMMAS -- III. GLOBAL LIMITING BEHAVIOR OF Sn -- IV. LOCAL LIMITING BEHAVIOR OF Sn -- V. SOME EXAMPLES OF K-L ORDERED FAMILIES -- VI. TWO SPECIAL FAMILIES -- VII. IMPLICATIONS FOR THE ESTIMATION OF θ0 -- VIII. CONCLUDING REMARKS -- REFERENCES -- CHAPTER 16. ON SOME RECURSIVE RESIDUAL RANK TESTS FOR CHANGE-POINTS -- I. INTRODUCTION -- II. RECURSIVE RESIDUAL RANK TESTS FOR THE LOCATION MODEL -- III. RECURSIVE RESIDUAL RANK TESTS FOR THE REGRESSION MODEL -- IV. ASYMPTOTIC PROPERTIES OF Dn+ AND Dn -- V. ASYMPTOTIC RELATIVE EFFICIENCY RESULTS -- VI. APPENDIX -- VII. ACKNOWLEDGMENT -- VIII. REFERENCES -- CHAPTER 17. OPTIMAL UNIFORM RATE OF CONVERGENCE FOR NONPARAMETRIC ESTIMATORS OF A DENSITY FUNCTION OR ITS DERIVATIVES -- I. INTRODUCTION -- II. PROOF OF THEOREM 2 -- REFERENCES -- CHAPTER 18. RANKS AND ORDER STATISTICS -- I. INTRODUCTION -- II. THE RESULT -- III. PROOF -- IV. APPENDIX -- V. REFERENCES -- PART IV: STATISTICAL GRAPHICS -- CHAPTER 19. M AND N PLOTS -- I. INTRODUCTION -- II. EXAMPLES OF M AND N PLOTS -- III. SOME PRACTICAL DETAILS -- IV. ACKNOWLEDGMENT -- V. REFERENCES -- CHAPTER 20. INVESTIGATING THE SPACE OF CHERNOFF FACES -- I. AN EMPIRICAL METHOD FOR EVALUATING REGIONS OF THE SPACE OF FACE PARAMETER VECTORS -- II. AN EMPIRICAL METHOD FOR ASSIGNING COORDINATES TO FACIAL FEATURES -- III. CONCLUSIONS.

ACKNOWLEDGMENTS -- REFERENCES -- CHAPTER 21. ON MULTIVARIATE DISPLAY -- Tables -- Inside-Out Plots -- Function Plots -- Polygons -- Trees -- Faces -- Extensions -- Conclusions -- Seeing vs. Reading a Display -- An Appreciation -- Acknowledgments -- References -- PART V: OTHER TOPICS -- CHAPTER 22. MINIMAX ESTIMATION OF THE MEAN OF A NORMAL DISTRIBUTION SUBJECT TO DOING WELL AT A POINT -- SUMMARY -- I. THE PROBLEM -- II. OPTIMAL AND SUBOPTIMAL PROCEDURES AND THE CONNECTION TO ROBUST ESTIMATION OF LOCATION -- III. THE BEHAVIOUR OF μ (t) FOR SMALL t -- IV. THE BEHAVIOUR OF μ (t) FOR t CLOSE TO 1 -- V. ACKNOWLEDGMENT -- VI. REFERENCES -- CHAPTER 23. SOME NEW DICHOTOMOUS REGRESSION METHODS -- I. INTRODUCTION -- II. MODELS FOR PREDICTING THE OUTCOME OF INTENSIVE CARE -- III. ANALOGIES TO NORMAL REGRESSION AND R2 -- IV. A SCREENING PROCEDURE FOR GOODNESS OF FIT -- V. EXAMINATION OF THE LIKELIHOOD SURFACE -- VI. DISCUSSION AND CONCLUSION -- ACKNOWLEDGMENT -- REFERENCES -- CHAPTER 24. THE APPLICATION OF SPLINE FUNCTIONS TO THE PHARMACOKINETIC ANALYSIS OF METHOTREXATE INFUSED INTO MALIGNANT EFFUSIONS -- I. INTRODUCTION -- II. ANALYSIS AND RESULTS -- III. DISCUSSION -- IV. ACKNOWLEDGMENTS -- V. REFERENCES -- CHAPTER 25. SELECTING REPRESENTATIVE POINTS IN NORMAL POPULATIONS -- REFERENCES -- CHAPTER 26. LEAST INFORMATIVE DISTRIBUTIONS -- I. INTRODUCTION -- II. THE NORMAL DISTRIBUTION -- III. THE CASE n = 2 -- IV. EXPONENTIAL DISTRIBUTION -- V. A MINIMAX FORMULATION -- VI. REFERENCES -- CHAPTER 27. SIGNIFICANCE LEVELS, CONFIDENCE LEVELS, CLOSED REGIONS, CLOSED MODELS, AND DISCRETE DISTRIBUTIONS -- I. INTRODUCTION -- II. TESTS -- III. CONFIDENCE PROCEDURES -- IV. REMARKS -- REFERENCES.

Recent Advances in Statistics: Papers in Honor of Herman Chernoff on His Sixtieth Birthday is a collection of papers on statistics in honor of Herman Chernoff on the occasion of his 60th birthday. Topics covered range from sequential analysis (including designs) to optimization (including control theory), nonparametrics (including large sample theory), and statistical graphics. Comprised of 27 chapters, this book begins with a discussion on optimal stopping of Brownian motion, followed by an analysis of sequential design of comparative clinical trials. A two-sample sequential test for shift with one sample size fixed in advance is then presented. Subsequent chapters focus on set-valued parameters and set-valued statistics; large deviations of the maximum likelihood estimate in the Markov chain case; the limiting behavior of multiple roots of the likelihood equation; and optimal uniform rate of convergence for nonparametric estimators of a density function and its derivatives. The book concludes by considering significance and confidence levels, closed regions and models, and discrete distributions. This monograph should be of interest to students, researchers, and specialists in the fields of mathematics and statistics.

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