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检验单个协方差矩阵结构的稳健方法AI 解读

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…

增长曲线模型中的协变量选择AI 解读

The growth curve model introduced by Potthoff & Roy (1964) is a generalization of the multivariate analysis of variance model and is often employed to analyze longitudinal data, in which a single characteristic has been measured at p different occasions on each individual. Inferential problems of this model are studied by using analysis of covariance, i.e. partitioning the p measurements into the measurements of q response variables and p-q covariables. Rao (1965, 1966) and…

多个群组共同主成分子空间的检验AI 解读

SUMMARY An approximate test, based on sample eigenprojections, is obtained for testing the hypothesis that the subspaces spanned by the first m principal components of several different covariance matrices are identical. This procedure can fairly easily be extended to an analogous test of hypothesis concerning correlation matrices. Extensions to a robust principal components analysis are also considered.

风险率变点的统计推断AI 解读

We discuss inference based on the likelihood ratio process for a hazard rate change point. A random change of time scale transforms the empirical process into a Poisson process which enables us to derive large deviation approximations to the significance level of the likelihood ratio test. We derive approximate confidence regions for the change point and joint confidence regions for the change point and size of change. The effect of censorship is also discussed. The methods…

含随机效应的广义线性模型估计AI 解读

A conceptually very simple but general algorithm for the estimation of the fixed effects, random effects, and components of dispersion in generalized linear models with random effects is proposed. Conditions are described under which the algorithm yields approximate maximum likelihood or quasi-maximum likelihood estimates of the fixed effects and dispersion components, and approximate empirical Bayes estimates of the random effects. The algorithm is applied to two data sets…

利用病例对照数据拟合前瞻性回归模型AI 解读

We consider fitting prospective regression models to data obtained by case-control or response selective sampling from a finite population with known population totals in each response category. Maximum likelihood estimation is developed and compared with two pseudo-likelihood approaches. The relative efficiencies of the methods are explored in the special case of estimating the parameters of the proportional odds model for ordinal responses. For such applications the method…

两个概率分布离散程度相等的检验AI 解读

Based on independent random samples from two distributions we consider the problem of testing that the distributions are identical except for an unknown location parameter against the alternative that one is less dispersed than the other. The proposed tests are shown to be asymptotically distribution-free and consistent. The asymptotic relative efficiencies with respect to several other tests for some specific alternatives are given.

自回归移动平均模型阶数估计札记AI 解读

A method for the estimation of parameters and model orders in an autoregressive-moving average system was introduced by Hannan & Rissanen (1982). That method may overestimate the model orders. Here an information theoretic order estimation procedure is introduced and shown to be consistent. Simulations show that the method performs well for moderate sample sizes.

光滑函数边际尾概率的近似及其贝叶斯与条件推断应用AI 解读

This paper presents an asymptotic approximation of marginal tail probabilities for a real-valued function of a random vector, where the function has continuous gradient that does not vanish at the mode of the joint density of the random vector. This approximation has error O(n−3/2) and improves upon a related standard normal approximation which has error O(n−½). Derivation involves the application of a tail probability formula given by DiCiccio, Field & Fraser (1990) to an…

存在误分类的二元数据假设检验：分析与试验设计AI 解读

SUMMARY Consider a binary random variable having outcomes subject to misclassification errors where the probabilities of misclassification errors depend on outcome. The asymptotic relative efficiencies are derived for comparing two binomial populations, comparing stratified binomial populations and for paired comparisons. The probabilities of misclassification can vary with strata or be different for each pair. The criterion for optimum experimental designs is shown to be…

Numerical simulations recently reported in the literature have shown that the profile likelihood associated with the estimation of covariance range parameters for a Gaussian field can be multimodal. Here we complement these recent results by considering covari-ances with unknown nugget, scale and range parameters. Estimation is performed in a restricted maximum likelihood framework. For unbounded sampling domains and known range parameter, conditions ensuring asymptotic…

高效的偏差校正非参数谱估计AI 解读

We consider estimation of a spectral density at a particular frequency. A linear model is developed based on the local second order behaviour of kernel spectral estimates and a second stage estimate is derived from this model. The estimate is shown to be asymptotically more efficient than the kernel estimate with the optimal, but unknown, bandwidth whenever the smoothing parameter is chosen so that it oversmooths the kernel estimate. A small-sample simulation study shows…

This paper considers tests of the null hypothesis of a unit root in an observed time series against the alternative that the series is level stationary. Interpolation tests whose critical values depend upon the value of the drift parameter are compared to the standard Dickey-Fuller tests in Monte Carlo simulations. The interpolation test performs quite well especially against one-sided alternatives.

重度删失数据下处理效应的一般估计量AI 解读

A generalized Hodges-Lehmann type estimator for the treatment effect in the two-sample problem with right censoring, is proposed based on an inverse-quantile-type idea using truncated versions of the Kaplan-Meier estimators over the subspace where they are consistent. Its strong consistency and asymptotic normality can be obtained, under no conditions on the uninformative censorings, and the resulting variance is easily estimable from the data. In simulation studies the…

关于交互作用检验中秩变换的一则注记AI 解读

SUMMARY The asymptotic properties of the rank transform statistic for testing for interaction in a balanced two-way classification are studied. Necessary and sufficient conditions are obtained for the asymptotic distribution of this rank transform statistic to be chi-squared under the null hypothesis of no interaction. It is shown that the rank transform test statistic for interaction is asymptotically chi-squared, divided by its degrees of freedom, when there are exactly…

回归参数稳定性的贝叶斯显著性检验AI 解读

This paper presents a Bayesian significance test for stationarity of a regression equation using the highest posterior density credible set. In addition, a solution to the Behrens-Fisher problem is provided. From a Monte Carlo simulation study, it has been shown that the Bayesian significance test has stronger power than the Cusum and the Cusum of squares tests. The Bayesian significance test may be useful in detecting individual parameter nonstationarity.

含有序多分类响应的非参数贝叶斯生物测定AI 解读

Previous attempts at implementing fully Bayesian nonparametric bioassay have enjoyed limited success due to computational difficulties. We show here how this problem may be generally handled using a sampling based approach to develop desired marginal posterior distributions and their features. A useful extension is presented which treats the case of ordered polytomous response. Illustrative examples are provided.

相对风险回归中的残差图AI 解读

Martingale-based residuals proposed for proportional hazards regression by Barlow & Prentice (1988) are considered. Plots of such residuals against time are shown to exhibit systematic patterns which are not a priori predictable even when the model is appropriate. For the plots to be fully useful therefore account needs to be taken of the expected pattern under the model. A simple amendment is suggested.

有先验信息时区分两个竞争模型的最优实验设计AI 解读

The design of experiments for discriminating between two rival models in the presence of prior information is analyzed. The method of Atkinson & Fedorov is extended. A theorem derived from the Kiefer-Wolfowitz General Equivalence Theorem is used to construct and check optimal designs. Some examples are provided.

多元分析中处理效应与误差的条件推断AI 解读

Directional methods of conditional inference are applied to the multivariate analysis of variance. Exact and easily implemented tests are derived for treatment effect, error variance matrix, and treatment improvement. Each test provides a physical measure of the magnitude of the departure from expectation under the hypothesis and is conditional on the indicated direction of departure. For treatment effect the test provides a geometrically understandable alternative to tests…

乘法随机效应的准似然分析AI 解读

A quasi-likelihood approach similar to that described by Morton (1987) is found to be particularly simple in the case of measurements subject to two or more sources of multiplicative error. Still further simplification occurs when the effects of interest also are multiplicative. The multiplicative analogue of the balanced ‘split plot’ model is considered in detail: an analysis of gamma deviance replaces the familiar analysis of variance. The efficiency of the…

迈向可实施的贝叶斯非参数密度估计AI 解读

SUMMARY Nonparametric density estimators smooth the empirical distribution function and are sensitive to the choice of smoothing parameters. This paper develops an hierarchical Bayes formulation for the smoothing problem. The prior distribution for the density function is the logistic normal process, which is a logistic transform of a Gaussian process. The covariance of the Gaussian process is a smoothing kernel and has parameters that control the degree of smoothness. The…

长度偏倚数据的核密度估计AI 解读

A new kernel density estimator for length biased data which derives from smoothing the nonparametric maximum likelihood estimator is proposed and investigated. It has various advantages over an alternative method suggested by Bhattacharyya, Franklin & Richardson (1988): it is necessarily a probability density, it is particularly better behaved near zero, it has better asymptotic mean integrated squared error properties and it is more readily extendable to related problems…

欠拟合回归与时间序列模型中修正 AIC 的偏差AI 解读

The Akaike Information Criterion, AIC (Akaike, 1973), and a bias-corrected version, AICC(Sugiura, 1978; Hurvich & Tsai, 1989) are two methods for selection of regression and autoregressive models. Both criteria may be viewed as estimators of the expected Kullback-Leibler information. The bias of AIC and AICC is studied in the underfitting case, where none of the candidate models includes the true model (Shibata, 1980, 1981; Parzen, 1978). Both normal linear regression and…