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位置未知的指数分布尺度参数的替代估计量AI 解读

Let $X_1, X_2,\cdots, X_n$ be independent observations from an exponential distribution with an unknown location-scale parameter $(\mu, \sigma)$. Let $\bar{X} = n^{-1} \sum X_i$ and $M = \min X_i$. Under squared error loss the best location-scale equivariant estimator of $\sigma$ is $\bar{X} - M$, which agrees with the maximum likelihood estimator. Arnold (J. Amer. Statist. Assoc. 65 (1970) 1260-1264) and Zidek (Ann. Statist. 1 (1973) 264-278) have shown that $\bar{X} - M$ is…

改进等变估计量的方法AI 解读

Techniques for improving on equivariant estimators are described. They may be applied, although without assurance of success, whatever be the family of underlying distributions. The loss function is required to satisfy an intuitively reasonable condition but is otherwise arbitrary. One of these techniques amounts to a sample space, orbit-by-orbit analysis of the conditional expected loss given the orbit. It yields, when successful, a "testimator". A second technique obtains…