Optimizing Methods in Statistics

Proceedings of a Symposium Held at the Center for Tomorrow, the Ohio State University, June 14-16, 1971

Jagdish S. Rustagi

• Publisher: Academic Press
• Year: 2014
• Print ISBN:
  9780126045505
• eBook ISBN:
  9781483260341
• Topic: Mathematics
• Subtopic: Applied Mathematics
• Index: Mathematics

Optimizing Method in Statistics is a compendium of papers dealing with variational methods, regression analysis, mathematical programming, optimum seeking methods, stochastic control, optimum design of experiments, optimum spacings, and order statistics. One paper reviews three optimization problems encountered in parameter estimation, namely, 1) iterative procedures for maximum likelihood estimation, based on complete or censored samples, of the parameters of various populations; 2) optimum spacings of quantiles for linear estimation; and 3) optimum choice of order statistics for linear estimation. Another paper notes the possibility of posing various adaptive filter algorithms to make the filter learn the system model while the system is operating in real time. By reducing the time necessary for process modeling, the time required to implement the acceptable system design can also be reduced One paper evaluates the parallel structure between duality relationships for the linear functional version of the generalized Neyman-Pearson problem, as well as the duality relationships of linear programming as these apply to bounded-variable linear programming problems. The compendium can prove beneficial to mathematicians, students, and professor of calculus, statistics, or advanced mathematics.

Table of contents

• Front Cover
• Optimizing Methods in Statistics
• Copyright Page
• Table of Contents
• CONTRIBUTORS
• PREFACE
• CHAPTER 1. THE EFFICIENT ESTIMATION OF A PARAMETER MEASURABLE BY TWO INSTRUMENTS OF UNKNOWN PRECISIONS
• CHAPTER 2. OPTIMIZATION PROBLEMS IN SIMULATION
• CHAPTER 3. SOME OPTIMIZATION PROBLEMS IN PARAMETER ESTIMATION
• CHAPTER 4. OPTIMAL DESIGNS AND SPLINE REGRESSION
• CHAPTER 5. ISOTONIC APPROXIMATION
• CHAPTER 6. ASYMPTOTICALLY EFFICIENT ESTIMATION OF NONPARAMETRIC REGRESSION COEFFICIENTS
• CHAPTER 7. COMPARISONS OF ORDER STATISTICS AND OF SPACINGS FROM HETEROGENEOUS DISTRIBUTIONS
• CHAPTER 8. MOMENT PROBLEMS WITH CONVEXITY CONDITIONS
• CHAPTER 9. VARIATIONAL METHODS IN ADAPTIVE FILTERING
• CHAPTER 10. NON LINEAR FILTERING
• CHAPTER 11. A CONVERGENCE THEOREM FOR NON NEGATIVE ALMOST SUPERMARTINGALES AND SOME APPLICATIONS
• CHAPTER 12. ON RELATIONSHIPS BETWEEN THE NEYMAN-PEARSON PROBLEM AND LINEAR PROGRAMMING
• CHAPTER 13. STATISTICAL CONTROL OF OPTIMIZATION
• CHAPTER 14. CURRENT CAPABILITIES IN MATHEMATICAL PROGRAMMING
• CHAPTER 15. PATTERNS AND SEARCH STATISTICS
• CHAPTER 16. NECESSARY CONDITIONS FOR A LOCAL OPTIMUM WITHOUT PRIOR CONSTRAINT QUALIFICATION
• CHAPTER 17. MATHEMATICAL MODELS FOR STATISTICAL DECISION THEORY1
• CHAPTER 18. CHANCE-CONSTRAINED PROGRAMMING:AN EXTENSION OF STATISTICAL METHOD
• CHAPTER 19. STOCHASTIC ALLOCATION OF SPARE COMPONENTS
• CHAPTER 20. OUTLIER PRONENESS OF PHENOMENA AND OF RELATED DISTRIBUTIONS
• CHAPTER 21. PROBLEM AREAS REQUIRING OPTIMIZING METHODS
• CHAPTER 22. STOCHASTIC APPROXIMATION
• CHAPTER 23. ALLOCATION OF OBSERVATIONS IN RANKING AND SELECTION WITH UNEQUAL VARIANCES
• CHAPTER 24. SEQUENCES OF MINIMAL FRACTIONS OF2n DESIGNS OF RESOLUTION V
• CHAPTER 25. OPTIMUM INTERVAL ESTIMATION FOR THE LARGEST SCALE PARAMETER
• CHAPTER 26. c-SAMPLE TESTS OF HOMOGENEITY AGAINST ORDERED ALTERNATIVES
• PARTICIPANTS