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位置参数的最优稳健线性估计量AI 解读

Efficiency-robust linear estimation as outlined in Birnbaum and Laska (JASA, 62 (1967) pp. 1230–1240) is applied, determining maximin-efficient linear unbiased estimators (MLUEs), and their efficiencies, for ordered samples of sizes 5 (5) 20 from a family of nine distributions. The results are compactly summarized because of the tendency of these distributions to admit simple orderings such that the MLUE over any subset of the distributions is just the MLUE over the extreme…

位置参数的渐近稳健估计量AI 解读

For the problem of efficiency-robust estimation of location, approximate versions are developed of optimally robust Pitman-type estimators. These are shown to have full asymptotic efficiency for a prototype family of distributions, used to define the estimators. The asymptotic efficiency under other distributions of interest is also characterized. For sample sizes n = 20, 30, 40, 50, and 100 the efficiencies were estimated by Monte Carlo methods under the following…

最优稳健性：一般方法及其在线性位置估计中的应用AI 解读

A general method of determining efficiency-robust estimation and testing methods is presented. This is used to derive admissible linear unbiased estimators (ALUEs) having the following optimality property: Over a specified (finite) family of possible symmetric shapes of the error distribution, the estimator's respective variances cannot be jointly improved. Such estimators are generalizations of Lloyd's best linear unbiased estimators (BLUEs) determined for single shapes.…

效率稳健的两样本秩检验AI 解读

In the classical two sample problem, the null hypothesis of identical distribution functions is tested. Rank testing procedures have the property that they are valid (have Type I error identically equal to α) for any absolutely continuous distribution function. Choices among rank tests are usually based upon local power calculations for a given specified null distribution against specific parametric alternatives. A rank test is said to be efficiency robust when no other has…

效率稳健的两样本秩检验AI 解读

In the classical two sample problem, the null hypothesis of identical distribution functions is tested. Rank testing procedures have the property that they are valid (have Type I error identically equal to α) for any absolutely continuous distribution function. Choices among rank tests are usually based upon local power calculations for a given specified null distribution against specific parametric alternatives. A rank test is said to be efficiency robust when no other has…

最优稳健性的一般方法及其在线性位置估计中的应用AI 解读

A general method of determining efficiency-robust estimation and testing methods is presented. This is used to derive admissible linear unbiased estimators (ALUEs) having the following optimality property: Over a specified (finite) family of possible symmetric shapes of the error distribution, the estimator's respective variances cannot be jointly improved. Such estimators are generalizations of Lloyd's best linear unbiased estimators (BLUEs) determined for single shapes.…

统计推断的基础AI 解读

The concept of conditional experimental frames of reference has a significance for the general theory of statistical inference which has been emphasized by R. A. Fisher, D. R. Cox, J. W. Tukey, and others. This concept is formulated as a principle of conditionality, from which some general consequences are deduced mathematically. These include the likelihood principle, which has not hitherto been very widely accepted, in contrast with the conditionality concept which many…

置信曲线：统一估计与统计假设检验的方法AI 解读

A standard practice of physical scientists is to report estimates (“measurements”) accompanied by their standard errors (or alternatively “average errors” or “probable errors”). Such reports are interpreted flexibly as appropriate in various contexts of application. With the usual normality assumption, such reports may be read as representing confidence intervals or limits at the various confidence levels, and this omnibus character largely accounts for the convenience and…

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