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修订与勘误：非负随机变量均值的无分布下置信限AI 解读

M. Breth, J. S. Maritz, E. J. Williams, Amendments and Corrections: On Distribution-Free Lower Confidence Limits for the Mean of a Nonnegative Random Variable, Biometrika, Vol. 66, No. 3 (Dec., 1979), p. 689

关于非负随机变量均值的分布无关置信下限AI 解读

M. BRETH, J. S. MARITZ, E. J. WILLIAMS; ‘On distribution-free lower confidence limits for the mean of a nonnegative random variable’, Biometrika, Volume 66

位置参数精确稳健置信区间札记AI 解读

The use of a simple permutation argument to set exact confidence limits for the location parameter of a symmetric distribution is described. The argument is applied to estimates based on original observations and on ranks and to M-estimates.

摘要暂缺

非负随机变量均值的分布无关置信下限AI 解读

A method for setting a distribution-free lower confidence limit for the mean of a non-negative random variable is developed, and compared with the procedure which relies on asymptotic normality of the distribution of the sample mean.

基于 U 统计量的位置估计量AI 解读

Let $X_1, \cdots, X_n$ be i.i.d. $F$, and estimate the median of $F$ by the median $T_\beta$ of $\beta X_i + (1 - \beta)X_j, i \neq j$, where $\beta$ is a fixed positive constant. Then $T_\beta$ is the solution of a $U$-statistic equation from which its asymptotic normality is readily derived. The asymptotic relative efficiency of $T_\beta$ is computed for a few cdfs $F$ and seen to be reasonably high for unintuitive choices such as $\beta = .9, \beta = 2$, and also to be…

Summary An empirical Bayes estimator which can be constructed without explicit estimation of the prior distribution is called a simple empirical Bayes estimator. Construction of such estimators for a single unknown parameter of a general continuous distribution is considered. Examples are given and their performance is examined.

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泊松分布的经验贝叶斯估计AI 解读

SUMMARY A number of established methods of empirical Bayes estimation for the Poisson distribution are surveyed, and their performances are compared. A new method of smooth empirical Bayes estimation is presented, and its performance is also studied. The question of assessing the effectiveness of the empirical Bayes approach in practice is examined.

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假设检验与复合决策问题的平滑经验贝叶斯方法AI 解读

The smooth empirical Bayes approach is based on using past observations to estimate a specified type of approximation to the prior distribution. This approach is applied to problems of empirical Bayes hypothesis testing and to the compound decision problem. Problems involving composite hypotheses are considered which have, hitherto, received much less attention than the case of two simple hypotheses. The methods are shown to be asymptotically optimal and results of studies…

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连续分布的平滑经验贝叶斯估计AI 解读

Although the conditions for application of the technique of empirical Bayes estimation of the parameter of a distribution may exist, the form of the prior distribution is generally unknown. This often creates major difficultics in the determination of empirical Bayes estimators. The simple device of approximating the prior distribution by a stop function is used to overcome this problem and to obtain smooth empirical Bayes estimators. This paper supplements earlier work by…

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单参数离散分布的平滑经验贝叶斯估计AI 解读

A study is made of the simple empirical Bayes estimators proposed by Robbins (1956). These estimators are compared with ‘best’ conventional estimators in terms of their expected squared error ‘loss’. The object of the study is to determine the amount of prior data which would be needed for the empirical Bayes estimator to be preferred to the conventional estimator. It is concluded that the required number of previous observations is likely to be too large for the simple…