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多项分布与列联表检验的功效和强度AI 解读

The strength of a significance test is defined as a weighted average of the power especially if the weights are a prior density. The concept is a compromise between Neyman-Pearsonian and Bayesian methods and is applied to tests for multinomial equiprobability and for no association in contingency tables. The differences of the power functions of two criteria, X 2 and G, are illustrated for the trinomial, where G arose earlier from a partially Bayesian approach. Other methods…

基于最大似然的循环配对设计方差分析AI 解读

A class of two-way random-effects models is presented for analyzing data that arise in a large variety of round robin designs. Examples of such designs can be found in numerous games, tournaments, and social interactions. The proposed models provide information not only about individual differences but also about the mutual contingency of the behaviors of interaction dyads. The statistical inference of the linear effects is discussed and a converging algorithm based on the…

对称矩阵求导及其应用AI 解读

Dwyer (1967) provided extensive formulas for matrix derivatives, many of which are for derivatives with respect to symmetric matrices. The results of his article are only for symmetric matrices whose (j, i) element is considered to differ from the (i, j) element even though their scalar values are equal. A simple result is given that extends the use of Dwyer's formulas to symmetric matrices in which the (i, j) element is considered functionally equal to the (j, i) element.…

一种简单的预测密度函数AI 解读

An easily computable predictive density is considered. Although involving a plain maximum likelihood technique, it coincides with the posterior predictive density with a noninformative prior. For standard situations achievements are comparable with classical inference.

关于无偏的 Lp 回归估计量AI 解读

Consider the familiar linear model y = Xβ + e. In an ingenious article by Sielken and Hartley (1973) it was shown how one can construct a computational scheme that will generate unbiased L 1 or L ∞ estimators even when multiple solutions exist. In a recent paper, Harvey (1978) provides a simple proof of unbiasedness for Lp estimators, 1 < p < ∞, under the assumption that the linear model is of full column rank; this insures that the estimator is unique. In this note it is…

光滑权重函数下 L 统计量的刀切法AI 解读

The behavior of linear combinations of order statistics (L-statistics) under jackknifing is discussed. The asymptotic behavior of a jackknifed L-statistic is described and the pseudovalue-based variance estimate is shown to be consistent under moderate smoothness and a trimming condition on the weight function. The results extend easily to functions of L-statistics and thus answer a question posed in Miller (1974). Monte Carlo results support small-sample applicability of…

随机有序变量生存函数的极大似然估计AI 解读

Many times, aspects of populations exist that must satisfy a stochastic ordering requirement. Nevertheless, estimates may not bear out this stochastic ordering because of the inherent variability of the observations. This article will consider the problem of finding maximum likelihood estimates of stochastically ordered survival functions for the cases (a) one survival function being fixed in advance and (b) estimating two survival functions when the data include censored…

利用时间序列与横截面数据估计具有正负边际风险的生产函数AI 解读

Two production-function models with error components for time and firms and a heteroscedastic disturbance are proposed. Unlike previous models, these two permit the variance of output to increase or decrease as one of the inputs is increased. When the models and some suggested estimators are applied to the pastoral zone of eastern Australia, the results indicate that labor, water, and possibly fencing, are likely to reduce the variance of wool production; and that sheep, and…

指数寿命部件构成的高可靠相干系统的置信限AI 解读

A method for constructing upper confidence limits (UCL's) for parametric functions of type g(λ) = Σ j Π i∈Ij λ i is considered. It is based on maximization of g(λ) over a confidence set of type {λ | Σ λiTi ≤ Λα & λ i ≥ 0} obtained by pooling statistical data received from separate testing of system components. An asymptotic representation of the reliability function of an arbitrary coherent system is given assuming that the element failure rates are low. It has the form R(t)…

基于相对位置的一类无分布双样本检验AI 解读

We consider a class of two-sample distribution-free tests that are appropriate for situations where one of the sample sizes is large relative to the other. These procedures are based on the placements of the observations in the smaller sample among the ordered observations in the larger sample, and this class of tests generalizes the Mann-Whitney (1947) procedure in much the same way that the class of linear rank tests generalizes the equivalent Wilcoxon (1945) rank sum…

与Hodges–Lehmann估计量相关的非对称性检验AI 解读

One version of the Hodges-Lehmann estimator, = median{(Xi + Xj )/2, 1 ≤ i, j ≤ n}, is also the minimum distance estimator derived from a particular Cramér-von Mises distance. This distance evaluated at , that is, the minimized distance, provides a natural statistic for testing asymmetry of the underlying distribution.

分布对称性的检验AI 解读

Tests for symmetry of a distribution function about an unknown value are investigated. The asymptotic distributions under symmetry as well as under near alternatives are given for two kinds of tests: trimmed Wilcoxon tests and tests based on gaps. It turns out that these procedures have a good stability of level under unimodal densities. In a special case (skewness to the left) the efficacies have been calculated. Monte Carlo results are also given.

利用分组数据估计相关系数AI 解读

This article proposes two estimators of the correlation coefficient, ρ, when statisticians will not construct a master file on individuals because of confidentiality issues. The approach depends on grouping the data according to the values of one of the variables. Group means and total variance for both variables are required to calculate the estimators. The complete bivariate sample need never be compiled. The estimators are shown to be asymptotically normal. Asymptotic and…

高效的有界影响回归估计AI 解读

The least squares estimator for β in the classical linear regression model is strongly efficient under certain conditions. However, in the presence of heavy-tailed errors and/or anomalous data, the least squares efficiency can be markedly reduced. In this article we propose an estimator that limits the influence of any small subset of the data and show that it satisfies a first-order condition for strong efficiency subject to the constraint. We then show that the estimator…

利用 Akaike 准则选择经济时间序列模型AI 解读

In this article we use the procedures introduced by Akaike (1974, 1976) and Schwarz (1978) to investigate the optimal specification of autoregressive moving average (ARMA) models for a group of major economic time series (see also Fine and Hwang 1979; Sawa 1978; Kashyap 1977; Leamer 1979; Chow 1979). The basic question we ask is whether the short AR representations that are estimated on an ad hoc basis in economics are validated by these more objective criteria. The article…

月度时间序列的日历效应：建模与调整AI 解读

Most monthly time series that represent a total of some variable for each month contain calendar effects due to changing month length, day-of-the-week effects, and holidays. It is important to remove the calendar variation to allow an effective assessment of the variation due to important factors. New procedures for calendar adjustment are presented in this article. A plausible model for the daily data is used to derive a model for the monthly data in which the power…

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对称矩阵求导及其应用AI 解读

Dwyer (1967) provided extensive formulas for matrix derivatives, many of which are for derivatives with respect to symmetric matrices. The results of his article are only for symmetric matrices whose (j, i) element is considered to differ from the (i, j) element even though their scalar values are equal. A simple result is given that extends the use of Dwyer's formulas to symmetric matrices in which the (i, j) element is considered functionally equal to the (j, i) element.…

利用分组数据估计相关系数AI 解读

This article proposes two estimators of the correlation coefficient, ρ, when statisticians will not construct a master file on individuals because of confidentiality issues. The approach depends on grouping the data according to the values of one of the variables. Group means and total variance for both variables are required to calculate the estimators. The complete bivariate sample need never be compiled. The estimators are shown to be asymptotically normal. Asymptotic and…