Unbiased Estimators and Their Applications: Volume 1: Univariate Case [Paperback]

Statistical inferential methods are widely used in the study of various physical, biological, social, and other phenomena. Parametric estimation is one such method. Although there are many books which consider problems of statistical point estimation, this volume is the first to be devoted solely to the problem of unbiased estimation. It contains three chapters dealing, respectively, with the theory of point statistical estimation, techniques for constructing unbiased estimators, and applications of unbiased estimation theory. These chapters are followed by a comprehensive appendix which classifies and lists, in the form of tables, all known results relating to unbiased estimators of parameters for univariate distributions. About one thousand minimum variance unbiased estimators are listed. The volume also contains numerous examples and exercises.
This volume will serve as a handbook on point unbiased estimation for researchers whose work involves statistics. It can also be recommended as a supplementary text for graduate students.
I. Elements of the Theory of Point Statistical Estimation.- 1. The Problem of Point Statistical Estimation.- 2. Risk of a Statistical Estimator.- 3. Consistency.- 4. Unbiasedness.- 5. Examples.- 6. Order Statistics.- 7. Empirical Distribution Function.- 8. Sufficient Statistics.- 9. The Information Inequality.- 10. The RaoBlackwellKolmogorov Theorem.- 11. Maximum Likelihood Estimation.- 12. The Method of Moments.- 13. Equivariant Estimators.- 14. Techniques for Improving Estimators.- 15. Unbiasedness in the Mean, and Other Concepts of Unbiasedness.- 16. Some Problems of Unbiased Estimation for the Normal Distribution.- I. Elements of the Theory of Point Statistical Estimation.- 1. Introducing a Factor Deleting the Bias.- 2. The RaoBlackwellKolmogorov Method.- 3. Estimators Based on the Unbiased Probability Density Function Estimator.- 4. Techniques Based on the Equation of Unbiasedness.- 5. Unbiasedl#)