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基于重抽样的假设检验的蒙特卡洛评价
Monte Carlo estimation of the power of tests that require resampling can be very computationally intensive. It is possible to reduce the size of the inner resampling loop as long as the resulting estimator of power can be corrected for bias. A simple linear extrapolation method is shown to perform well in correcting for bias and thus reduces computation time in Monte Carlo power studies.
在干扰参数置信集合上最大化的 p 值
For testing problems of the form H 0: v = v 0 with unknown nuisance parameter θ, various methods are used to deal with θ. The simplest approach is exemplified by the t test where the unknown variance is replaced by the sample variance and the t distribution accounts for estimation of the variance. In other problems, such as the 2 × 2 contingency table, one conditions on a sufficient statistic for 0 and proceeds as in Fisher's exact test. Because neither of these standard…
协方差矩阵同质性检验的自助法临界值
Bartlett's modified likelihood ratio statistic A is often suggested in multivariate analysis for testing equality of covariance matrices. Unfortunately, the χ 2-approximation to the null distribution of −2 log Λ is useful only when the data is normally distributed. This article presents a pooled bootstrap procedure that replaces the χ 2-approximation and makes Bartlett's statistic a useful tool for data analysis. This procedure also applies to most quadratic form test…
协方差矩阵同质性检验的 Bootstrap 临界值
Bartlett's modified likelihood ratio statistic A is often suggested in multivariate analysis for testing equality of covariance matrices. Unfortunately, the χ 2-approximation to the null distribution of −2 log Λ is useful only when the data is normally distributed. This article presents a pooled bootstrap procedure that replaces the χ 2-approximation and makes Bartlett's statistic a useful tool for data analysis. This procedure also applies to most quadratic form test…
贝叶斯分析中的适当似然
The validity of posterior probability statements follows from probability calculus when the likelihood is the density of the observations. To investigate other cases, a second, more intuitive definition of validity is introduced, based on coverage of posterior sets. This notion of validity suggests that the likelihood must be the density of a statistic, not necessarily sufficient, for posterior probability statements to be valid. A convenient numerical method is proposed to…
贝叶斯分析中适当的似然函数
The validity of posterior probability statements follows from probability calculus when the likelihood is the density of the observations. To investigate other cases, a second, more intuitive definition of validity is introduced, based on coverage of posterior sets. This notion of validity suggests that the likelihood must be the density of a statistic, not necessarily sufficient, for posterior probability statements to be valid. A convenient numerical method is proposed to…
检验单个协方差矩阵结构的稳健方法
Patterns for a single covariance matrix may be studied using likelihood ratio or quadratic form test statistics. Typically these tests have an asymptotic chi-squared distribution when the data are normally distributed, but the asymptotic distribution is sensitive to nonnor-mality. This paper suggests two ways to robustify inference for patterned matrices: (i) estimate the critical values of normal theory test statistics using a new bootstrap procedure which takes advantage…
用线性秩统计量比较多个总体
There are many nonparametric tests available for the analysis of k independent samples. For example, the Kruskal—Wallis test (Wilcoxon rank sum test when k = 2) is widely used for detecting location differences, and Mood or Ansari—Bradley or Sigel—Tukey rank statistics are often suggested for detecting scale differences. If more general alternatives are of interest, then one can use omnibus tests such as the generalized Kolmogorov—Smirnov and Cramér—von Mises statistics [see…
利用先验信息的自助法
Bayesian analysis is subject to the same kinds of misspeciflcation problems which motivate the robustness and nonparametric literature. We present a method of incorporating prior information which performs well without direct knowledge of the error distribution. This is accomplished by replacing the likelihood in Bayes's formula by a bootstrap estimate of the sampling density of a robust estimator. The flexibility of the method is illustrated by examples, and its performance…
多元位置与协方差的最小 Hellinger 距离估计
The Hellinger distance between a nonparametric density estimator and a model family is minimized to produce estimates of location and covariance in multivariate data. With suitable restrictions on the density estimators and the model family, these minimum Hellinger distance estimators (MHDE's) are shown to be affine invariant, consistent, and asymptotically normal. The robustness of the MHDE as measured by the breakdown point compares favorably against the previously studied…
利用先验信息的自助法
Bayesian analysis is subject to the same kinds of misspeciflcation problems which motivate the robustness and nonparametric literature. We present a method of incorporating prior information which performs well without direct knowledge of the error distribution. This is accomplished by replacing the likelihood in Bayes's formula by a bootstrap estimate of the sampling density of a robust estimator. The flexibility of the method is illustrated by examples, and its performance…
与Hodges–Lehmann估计量相关的非对称性检验
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.
位置参数与拟合优度的最小距离估计
A weighted Cramér-von Mises distance between the empirical distribution function and the assumed model F0(x - θ) is minimized to produce estimators θ n that are asymptotically normal. If the weight function is taken proportional to (- ln f 0)″/f 0 , then θ n is asymptotically efficient and the minimized distance has the appropriate loss of one degree of freedom. Special attention is focused on the limiting distribution of this latter goodness-of-fit statistic in both null…
由 M 估计构造近似置信区间的新方法
The empirical function used to define M estimates of location is similar to a distribution function when Ψ is nondecreasing. This similarity allows approximate confidence intervals to be constructed from the “percentiles” of the defining function.
L 统计量的一种微分
The functional $T(F) = \int F^{-1}(t)J(t) dt$ associated with linear combinations of order statistics is shown to have a Frechet-type differential. As a corollary, the statistic $T(F_n)$ obtained by evaluating $T(\cdot)$ at the sample df $F_n$ is seen to be asymptotically normal and to obey a law of the iterated logarithm.