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成对排序与联合排序：再看 Kruskal–Wallis 统计量AI 解读

A test statistic for the k-sample location problem is constructed by appropriately combining all pairwise two-sample Wilcoxon tests. The result is an analogue of the Kruskal-Wallis statistic in the sense that the Pitman asymptotic relative efficiency between the two is one. However, the approximate Bahadur efficiency of the analogue relative to the Kruskal-Wallis statistic is shown to be greater than or equal to one at every alternative.

变点风险率模型似然中的一个奇异性AI 解读

A singularity identified by Nguyen, Rogers & Walker (1984) in the log likelihood function for a change-point hazard rate model is eliminated if the likelihood function is appropriately defined.

样本时空自协方差与自相关函数的矩AI 解读

Pfeifer & Deutsch (1981) have derived expressions for the means and variances of the sampled autocovariances and autocorrelations, in the case of a white-noise space-time process. This note shows how their work can be extended to general space-time autoregressive moving average processes. The results are useful for testing the significance of observed space-time autocorrelations, given a hypothesized space-time process.

依赖数据下的优势比推断AI 解读

When data can be presented as a series of k 2×2 tables with cell counts (xi ,ni−xi, yi, mi−yi), it is often assumed that xi and yi are binomially distributed. This paper deals with inference for the common odds ratio Ψ when the binomial assumption is invalid. When k increases, the consistency and asymptotic normality of the Mantel & Haenszel (1959) estimator is derived. The conditional maximum likelihood estimator is shown to be inconsistent and the asymptotic bias is…

相关测量误差下线性结构关系模型的估计AI 解读

Maximum likelihood estimators for model parameters in linear structural relationships having correlated measurement errors are presented. Comparisons between asymptotic mean squared errors of least squares and maximum likelihood estimators of the slope parameter indicate that the least squares estimator is only preferable when the slope parameter is sufficiently small relative to the ratio of error standard deviations; however, unlike structural relationships having…

有效得分统计量零假设分布的渐近展开AI 解读

An asymptotic expansion for the null distribution of the efficient score statistic for testing a composite hypothesis in the presence of nuisance parameters is derived, and an interpretation of the terms occurring in the expansion is given. The use of the expansion to modify the percentage points of the large-sample reference x2 distribution is discussed. The first three moments of the null distribution are obtained and are used as a check on the accuracy of the algebra via…

Given a sample from a distribution F supported on a p-dimensional sphere, several confidence cones for the ‘mean directional vector’ are proposed. Some methods have been available, but they depend on parametric assumptions. In this paper, nonparametric confidence cones based on the bootstrap are considered, and consistency of these methods is obtained under minimal conditions. We compare the performances of bootstrap methods with the others by Monte Carlo simulations.

统计推断与序贯设计AI 解读

If an experiment is designed sequentially, repeated-sampling inference may not necessarily be made using distributional results that are valid for fixed designs. A few simple illustrative examples and alternative approaches are given. Sometimes the sequential nature of design can be ignored asymptotically. Links are forged with inference for stochastic processes and missing data problems.

含缺失值的连续与分类混合数据的最大似然估计AI 解读

Maximum likelihood procedures for analysing mixed continuous and categorical data with missing values are presented. The general location model of 01kin & Tate (1961) and extensions introduced by Krzanowski (1980, 1982) form the basis for our methods. Maximum likelihood estimation with incomplete data is achieved by an application of the EM algorithm (Dempster, Laird & Rubin, 1977). Special cases of the algorithm include Orchard & Woodbury's (1972) algorithm for incomplete…

顺序约束推断中 Bartholomew 统计量零假设分布的若干近似AI 解读

Approximations are proposed for the null distribution of Bartholomew's Ē2for testing the homogeneity of normal means against simple order alternative. Numerical comparison shows that our approximations give quite satisfactory results.

广义对数线性模型中改进似然比统计量的一则注记AI 解读

Cordeiro (1983) and williams (1976) have derived improved likelihood ratio statistics for log linear models. It is shown here that for the case of testing nested decomposable models, their results are equivalent.

对数秩检验中 Mantel–Haenszel 方差的适当性AI 解读

A challenge by Brown (1984) of the Mantel-Haenszel variance for the log rank test is dismissed as due to the nonasymptotic situation considered by Brown. Where the censoring mechanism in a time-to-response study could be influenced by treatment, the permutational variance is inappropriate and the Mantel-Haenszel hypergeometric variance must be used. If treatment is known or postulated to have no effect on the censoring mechanism, then use of the Mantel-Haenszel variance…

马氏距离与椭圆分布AI 解读

The Mahalanobis distance is shown to be an appropriate measure of distance between two elliptic distributions having different locations but a common shape. This extends a result long familiar in multivariate analysis to a class of nonnormal distributions. It can also be used to show that the sample version of the Mahalanobis distance is appropriate under both estimative and predictive approaches to estimation for the family of multivariate normal distributions differing…

估计线段强度时对边缘效应造成的计数偏差进行校正AI 解读

A formula is suggested for correcting segment or fibre counts for edge effects. The correction results in an unbiased estimate of segment intensity, provided only that the observation field is convex. No assumptions are made about the distribution of fibre length. A method is proposed for constructing confidence intervals for segment intensity, using the corrected segment count.

随机过程有限样本估计的基础AI 解读

The Gauss-Markov theorem on least squares for linear models derives its general applicability because it depends on the underlying distribution only through the first two moments. In this paper, a similar theorem is established within the context of stochastic processes. Various problems of finite sample estimation are solved by application of this theorem.

临床试验两时期交叉设计中的不完整数据分析AI 解读

A procedure for analysing a simple two-period crossover design is proposed when some observations at the second treatment period are missing. Using all available data, the maximum likelihood estimators of the parameters are obtained and approximate tests proposed under the assumption that the data come from bivariate normal populations. The performances of these tests are compared with those of Grizzle's tests which require complete pairs of observations, using Monte Carlo…

相关观测下重复测量设计的最优性与加权最小二乘分析AI 解读

We consider a model for repeated measurements designs where the measurements on the same unit are assumed to be correlated with known correlation coefficient. It is shown that Latin squares with an additional balancing property are E-optimal for the weighted least squares estimate.

调整协变量的删失生存数据组序贯检验AI 解读

Group sequential tests for the analysis of survival data that compare two treatments and allow for the adjustment of other concomitant variables are discussed. These methods allow early termination of a study if large treatment differences occur. Based on simulation results, we compare the operating characteristics of these adjusted tests with the unadjusted sequentially-computed log rank test.

不完整重复测量下相关检验的合并AI 解读

In comparing the effectiveness of two treatments, repeated measurements of the same characteristic are often taken under two or more distinct conditions for each experimental subject. A locally best linear combination of individual test statistics obtained under different conditions is proposed to test the equality of the two treatments. The test procedure allows different patterns of missing observations for the two groups to be compared. Special cases such as combining…

稀疏数据下优势比同质性的检验AI 解读

Three tests for homogeneity of odds ratio for a series of 2 × 2 tables when the data are sparse are studied by means of Monte Carlo experiments. A score test, based on the assumption that the log odds ratios are generated from some unknown distribution, is shown to be more powerful than the other two. The original test of Zelen (1971), later corrected by Halperin, Ware, Byar et al. (1977), is also examined. It tends to be too liberal under the sparse data situation; however,…

平稳单变量时间序列新息方差的频域估计AI 解读

The innovation variance σ2 of a linear stochastic time series model can be estimated using periodogram ordinates. However, since the periodogram ordinates as estimators of the corresponding spectrum ordinates can show appreciable small-sample bias, it is believed that the estimator of σ2 is biased. One way of reducing the small-sample bias in the periodogram ordinates is by tapering. In this paper an estimator of σ2 based on tapered time series is defined and evaluated…

典型分析在时间序列模型识别中的应用AI 解读

The second-order moment structure of time series models is used to derive a canonical analysis in time series modelling. Consistency properties of certain canonical correlations and the corresponding eigenvectors are shown. Based on these properties, a canonical correlation approach for tentative order determination in building autoregressive-moving average models is proposed. This approach can handle directly nonstationary as well as stationary processes and it also…

自回归模型中的正态性检验AI 解读

It is shown that any test of normality computed from autoregressive residuals has the same limiting null distribution as for the standard case of independent, identically distributed observations with estimated parameters. Some numerical results are given to indicate that this approximation is acceptable for sample size 20 in first- and second-order models. Limited numerical results are also given to explore the effect of incorrectly specifying the order.

用于评估依赖关系的 Chi 图AI 解读

This paper presents a graphical method to be used, in conjunction with a scatterplot, to investigate possible association of two variates as manifested in a sample of bivariate measurements. The method is designed so that the plot is approximately horizontal under independence, and under various forms of association it produces corresponding characteristic patterns. Examples given include application to study of regression residuals, dependence of two spatial point…