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方向数据的投影多元线性模型AI 解读

We introduce the spherically projected multivariate linear model for directional data. This model treats directional observations as projections onto the unit sphere of unobserved responses from a multivariate linear model. Focusing on the important case of circular data, we show that maximum likelihood estimates for the model are readily computed using iterative methods, in sharp contrast with competing approaches. Examples are given to demonstrate the resulting methodology…

单侧二项检验的合并AI 解读

Six methods of combining k independent binomial test statistics are compared with respect to their median significance levels, asymptotic relative efficiencies, and accuracy of null distribution approximations. The test statistics considered are the minimum significance level, Fisher's omnibus test, the likelihood ratio, an approximate likelihood ratio, the Mantel-Haenszel statistic, and the sum of chis. Fisher's test and the likelihood ratio perform relatively well for all…

单侧二项检验的合并AI 解读

Six methods of combining k independent binomial test statistics are compared with respect to their median significance levels, asymptotic relative efficiencies, and accuracy of null distribution approximations. The test statistics considered are the minimum significance level, Fisher's omnibus test, the likelihood ratio, an approximate likelihood ratio, the Mantel-Haenszel statistic, and the sum of chis. Fisher's test and the likelihood ratio perform relatively well for all…

R×C 析因配对比较实验的设计AI 解读

Two designs for R × C factorial paired comparison experimente are compared, assuming the Bradley-Terry model. One design employs comparisons of all paira of the RC treatments, and the other degign restricts comparisons to those pairs which have the same level of one factor. Computation of maximum likelihood estimates under several hypotheses is considered for each design. The restricted design has administrative benefits because it requires comparison of fewer distinct pairs…

两个正态总体均值与方差相等的检验AI 解读

Let X 1, …, X m and Y 1, …, Y n be two independent random samples from normal populations N(μ1, σ1 2) and N(μ2, σ2 2), respectively. The statistical problem is to test H 0: μ1 = μ2 and σ1 2 = σ2 2 against H a : μ1 ≠ μ2 or σ1 2 ≠ σ2 2. Using Fisher's method of combining two independent test statistics, we suggest a test and prove that it is asymptotically optimal in the sense of Bahadur efficiency.

两个正态总体均值与方差相等的检验AI 解读

Let X 1, …, X m and Y 1, …, Y n be two independent random samples from normal populations N(μ1, σ1 2) and N(μ2, σ2 2), respectively. The statistical problem is to test H 0: μ1 = μ2 and σ1 2 = σ2 2 against H a : μ1 ≠ μ2 or σ1 2 ≠ σ2 2. Using Fisher's method of combining two independent test statistics, we suggest a test and prove that it is asymptotically optimal in the sense of Bahadur efficiency.

基于 Kolmogorov–Smirnov 统计量的位移与对称中心估计AI 解读

A point estimator and a set of confidence intervals based on the Kolmogorov-Smirnov statistic are proposed for the shift parameter in the two-sample problem. Asymptotic distibution of the etimator as well as asymptotic bounds for the lengths of the intervals are derived. The two-sample results are then adapted to the one-sample problem to define an estimator and a set of confidence intervals for the center of a symmetric population.

Fisher独立检验合并方法的渐近最优性（二）AI 解读

It was shown by Littell and Folks [3] that Fisher's method of combining independent tests is asymptotically optimal among four commonly used methods of combining, according to Bahadur relative efficiency. The result of the present article is that Fisher's method is asymptotically optimal among essentially all methods of combining independent tests.

Fisher 独立检验合并方法的渐近最优性AI 解读

Four methods of combining independent tests of hypothesis are compared via exact Bahadur relative efficiency. The methods considered are Fisher's method, the mean of the normal transforms of the significance levels, the maximum significance level, and the minimum significance level. None of these is uniformly more powerful than the others, but, according to Bahadur efficiency, Fisher's method is the most efficient of the four. In some cases, Fisher's method is most efficient…