Variances of UMVU Estimators for Means and Variances After Using a Normalizing Transformation |
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| Authors: | Shimizu Kunio |
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| Institution: | Department of Information Sciences , Science University of Tokyo , Noda City, Chiba, 278, Japan |
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| Abstract: | Suppose that the function f is of recursive type and the random variable X is normally distributed with mean μ and variance α2. We set C = f(x). Neyman & Scott (1960) and Hoyle (1968) gave the UMVU estimators for the mean E(C) and for the variance Var(C) from independent and identically distributed random variables X1,…, Xn(n ≧ 2) having a normal distribution with mean μ and variance σ2, respectively. Shimizu & Iwase (1981) gave the variance of the UMVU estimator for E(C). In this paper, the variance of the UMVU estimator for Var(C) is given. |
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| Keywords: | recursive transformation variances of UMVU estimators for means and variances hypergeometric function |
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