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删失数据下双参数递减风险率分布的极大似然估计AI 解读

Problems of maximum likelihood estimation are discussed for shape and scale parameters from certain decreasing hazard rate distributions, typically either mixed-exponential or “work-hardened.” Sufficient conditions on the mixing distribution are given that guarantee regular behavior of the hazard rate and that ensure, even with highly censored data, that the MLE's exist from such DHR distributions whenever the sample satisfies a certain condition; otherwise a constant hazard…

双因素设计中的分布无关秩检验AI 解读

A class of distribution-free statistics using scores based on ranks for testing main effects in two-way layouts, with no interactions and more than one observation per cell, is discussed. Asymptotic distributions are developed under the null and alternative hypotheses for the case in which cell size is fixed and the number of blocks is allowed to become large, and as cell size becomes large with the number of blocks fixed. Efficiencies are considered under both asymptotic…

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线性贝叶斯估计量的一般方差修正AI 解读

We consider the problem of modifying the linear Bayes estimator for the mean of a distribution of unknown form by using an estimate of sample variance. The general conditions under which there is no advantageous variance modification to the linear Bayes rule are identified. These results are applied to the problem of sampling from a normal distribution with unknown mean and variance, and the implications are discussed.

面向使用者的统计推断AI 解读

A class of inferential procedures (called user-oriented procedures) related to the equal probability test of Arrow (1960) is introduced for use in many univariate problems. These procedures require that experimenters be able to interpret the parameters about which they wish to make inference. The class of procedures include confidence intervals associated with the equal probability test as well as an analogue to the P value. The confidence intervals are easier to interpret…

审理死刑案件的陪审团：一项法律程序的统计分析AI 解读

Potential jurors in capital cases are often queried on their attitudes toward capital punishment. The extreme groups say they would never or they would always approve capital punishment, given a guilty verdict. In many jurisdictions, these two groups are routinely excluded from juries deciding whether the defendant is guilty in capital cases. This exclusion persists even when the potential jurors say they could be fair and impartial in deciding guilt or innocence. The…

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A class of conditionally distribution-free rank order tests is developed for testing interchangeability of two correlated variates with incomplete data on both responses. Asymptotic properties of these tests are examined. In particular, we show that the proposed tests are also asymptotically distribution-free. For location alternatives, the Pitman efficiency of the rank order test relative to the parametric test based on the bivariate normal model is investigated.

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为多元一般线性模型生成特征可独立控制的测试数据AI 解读

Experiments to assess the performance characteristics, both of statistical methods and of computer programs that implement them, are best performed using test data with controlled statistical and numerical properties. We describe an algorithm for constructing test data for any multivariate linear model that provides complete control (subject only to the requirement of mutual consistency) over the following factors: regression coefficients; regression and residual sums of…

失效率函数的核估计与密度估计：一种类比AI 解读

In this article we explore methods by which the rate of convergence of the bias and the mean squared error of kernel estimators of the failure-rate function can be improved. We show that if the kernel is not restricted to be nonnegative and is suitably chosen, then the bias contribution to the asymptotic mean squared error can be eliminated to any required order, and the rate of convergence of the asymptotic mean squared error can be brought as close to n −1 as is desired.…

一类多元分析统计量的分布AI 解读

In this article, exact and asymptotic distributions of a class of statistics whose moments are of a particular form have been obtained. An application to Wilks's criterion for testing a linear hypothesis is given, and it is shown by numerical comparison that the first term of the asymptotic expansion of the distribution obtained in this article is better than Box's asymptotic expansion in terms of chisquared distributions. The exact distribution is easily computable and has…

具有共同线性部分的模型中误设离散矩阵下的线性估计AI 解读

The linear model (Y, Xβ, V), where X is any matrix satisfying the conditions ℛ (U) ⊂ ℛ (X) and ℛ (A′) ⊂ ℛ (X′), is considered, U and A being known matrices and ℛ (·) denoting range space. Nonnegative definite matrices V, for which every linear representation or some linear representation of the BLUE of Aβ under (Y, Xβ, V 1) continues to be its BLUE under (Y, Xβ, V) for every such matrix X, are characterized. Conditions under which estimable linear parametric functions admit…

正确选择概率的 Olkin-Sobel-Tong 估计量的小样本性质AI 解读

In the problem of selecting the best of k populations, Olkin, Sobel, and Tong (1976) have introduced the important idea of a posteriori analysis of the data (as opposed to the usual formulation), in which design of the experiment is the major consideration. They considered the large-sample properties of an estimator that has been discussed further by Gibbons, Olkin, and Sobel (1977), Gupta and Panchapakesan (1979), and Tong (1980). In this article we study the small-sample…

密度估计中修正似然准则的一个注记AI 解读

Let f λ be a kernel estimate (with window width λ) of the density f. Its performance is assessed by the Kullback-Leibler information distance I(f, f λ) = ∫ f log f − ∫ f log f λ. This article establishes conditions for the asymptotic equivalence of the cross-validation estimate and the jackknife estimate of the term ∫ f log f λ, and provides the common limiting value. This gives insight into the “modified likelihood” criterion for choosing λ, introduced by Habbema, Hermans,…

离散多元冲击模型的最大似然估计AI 解读

A k-variate Bernoulli distribution with k + 1 parameters is obtained as a shock model in which shocks are fatal to single components only or to all components simultaneously in a k-component system. The maximum likelihood estimator (MLE) for model parameters is fully characterized. In the most complex case, the MLE is displayed as a simple function of the smallest positive root of a kth degree polynomial. An iterative scheme that converges monotonically to the desired root…

作为证据的先验与似然比AI 解读

Arguments based on diagnostic data concerning a particular case, and ones based on prior experience with like cases, can be represented by belief functions and combined by Dempster's Rule. In limiting cases, the belief functions depend on likelihood ratio or on prior odds, and when these limiting cases occur together, Bayes' Theorem is applicable as is Dempster's Rule. The resulting functional equations lead to a single-parameter family of functions relating belief strength…

基于变换数据的统计检验AI 解读

The problem of testing hypotheses in linear models when the original data have been transformed is considered. It is assumed that the transformation involves an unknown parameter that has to be estimated from the data. For certain important testing problems it is found that the asymptotic level and power is as if λ had been assumed known. Asymptotic efficiency results show that when the Box-Cox transformation is used, tests based on transformed data have good power…