Table of Contents

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 Rao—Blackwell—Kolmogorov 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 Rao—Blackwell—Kolmogorov Method.- 3. Estimators Based on the Unbiased Probability Density Function Estimator.- 4. Techniques Based on the Equation of Unbiasedness.- 5. Unbiased Estimators of Parameters of Discrete Distributions.- 6. The Abbey and David Techniques.- III. Applications of Unbiased Estimation Theory.- 1. Unbiased Estimators of Parameters of Truncated Exponential and Normal Distributions, with Applications.- 2. Some Statistical Models and Estimators Useful in Integrated Circuit Quality Control.- 3. Unbiased Estimators in the Classical Occupancy Problem with Applications.- 4. Some Unbiased Estimators of the Reliability of Systems.- 5. Unbiasedness, Sufficiency, and a Chi-Square Goodness-of-Fit Test for Discrete Exponential Distributions of Rank One.- Tables of Unbiased Estimators.- A1. Unbiased Estimators of Functions of Parameters of the Normal Distribution.- A2. Unbiased Estimators of Functions of the Parameter ? of the Uniform Distribution.- A3. Unbiased Estimators of the Functions of the Parameter ? of the DiscreteUniform Distribution (Sampling with Replacement).- A4. Unbiased Estimators of Functions of the Parameter ? of the Discrete Uniform Distribution (Sampling without Replacement).- A5. Unbiased Estimators of Functions of the Parameter ? of the Gamma-Distribution.- A6. Unbiased Estimators of Functions of Parameters ? and ? of the Inverse Gaussian Distribution.- A7. Unbiased Estimators of Functions of Parameters of the Weibull Distribution.- A8. Unbiased Estimators of Functions of Parameters of the Rayleigh Distribution.- A9. Unbiased Estimators of Functions of Parameters of some Independent Normal Distributions.- A10. Unbiased Estimators of Functions of a Paramater of the Seminormal Distribution.- A11. Unbiased Estimators of Functions of Parameters of the Left-Truncated Exponential Distribution (? and ? are Unknown).- A12. Unbiased Estimators of Functions of Parameters of the Left-Truncated Exponential Distribution (? is Known).- A13. Unbiased Estimators of Functions of Parameters of the Paretian Law.- A14. Unbiased Estimators of Functions of Parameters of the Left-Truncated Exponential Distribution of a General Type.- A15. Unbiased Estimators of Functions of a Parameter of the Right-Truncated Exponential Distributions.- A16. Unbiased Estimators of Functions of Parameters of the Uniform Distribution with Two Unknown Parameters.- A17. Unbiased Estimators for Functions of a Parameter ? of the Extreme Value Distribution.- A18. Unbiased Estimators of Functions of Parameters of the Burr Distribution.- A19. Unbiased Estimators of Functions of Parameters of the Logarithmic-Power Distribution.- A20. Unbiased Estimators for Functions of Parameters ? and r of the Left-Truncated Power Series Distribution.- A21. Unbiased Estimators of Functions of Parameters ? and r of theLeft-Truncated Generalized Logarithmic Series Distribution.- A22. Unbiased Estimators of Functions of Parameters ? and r of the Left-Truncated Logarithmic Series Distribution.- A23. Unbiased Estimators of Functions of Parameters of the Truncated Geometrical Distribution.- A24. Unbiased Estimators of Functions of a Parameter ? of the Binomial Distribution.- A25. Unbiased Estimators of Functions of a Parameter ? of the Negative Binomial Distribution.- A26. Unbiased Estimators of Functions of Parameters of the Left-Truncated Generalized Negative Binomial Distribution.- A27. Unbiased Estimators of Functions of Parameters of the Left-Truncated Generalized Poisson and the Borel-Tanner Distribution.- A28. Unbiased Estimators of Functions of the Parameter ? of the Poisson Distribution.- A29. Unbiased Estimators of Functions of Parameters of the Left-Truncated Poisson Distribution.- A30. Unbiased Estimators of Functions of the Parameter ? of the Hypergeometric Distribution.- A31. Unbiased Estimators of Functions of the Parameter ? of the Negative Hypergeometric Distribution.- A32. Unbiased Estimators of Functions of Parameters of the Lognormal Distribution.- A33. UMVUE’s of Parameters for a Subclass of Stable Distributions.- A34. UMVUE’s of Parameters for the Stirling Distribution of the Second Kind.- References.

Promotional Information

Springer Book Archives