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随机变量上下界的最优线性估计AI 解读

The problem of estimating the bounds of random variables has been discussed by Cooke (1979). Here we discuss optimality of estimators when the data are censored so that only the r largest or smallest of the observations are available for estimating a bound. For fixed r we find the linear function of the censored data which is the optimal estimator of a bound in the sense that, when the sample size is large, the estimator has smallest mean squared error among all such linear…

随机变量边界的最优线性估计AI 解读

The problem of estimating the bounds of random variables has been discussed by Cooke (1979). Here we discuss optimality of estimators when the data are censored so that only the r largest or smallest of the observations are available for estimating a bound. For fixed r we find the linear function of the censored data which is the optimal estimator of a bound in the sense that, when the sample size is large, the estimator has smallest mean squared error among all such linear…

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随机变量边界的统计推断AI 解读

Robson & Whitlock (1964) considered point estimation and confidence limits for the upper bound of a random variable when the bound was known to be a truncation point. However, their approach to the point estimation problem failed to produce an estimator with smaller mean squared error than the largest order statistic from a random sample. In this paper we construct point estimators of the bounds of random variables which are substantially better estimators than the extreme…