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带置信集合的密度估计：星系超星系团与空洞示例AI 解读

A method is presented for forming both a point estimate and a confidence set of semiparametric densities. The final product is a three-dimensional figure that displays a selection of density estimates for a plausible range of smoothing parameters. The boundaries of the smoothing parameter are determined by a nonparametric goodness-of-fit test that is based on the sample spacings. For each value of the smoothing parameter our estimator is selected by choosing the normal…

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福利项目质量控制中的统计推断AI 解读

Federal and state agencies estimate rates of payment error made by state caseworkers in determining benefits under the Aid to Families with Dependent Children, Food Stamp, and Medicaid programs. Estimated payment error rates are used in turn to estimate program penalties that are a function of the difference between payment error rates and target rates. This article first outlines the statistical methodology currently used in welfare quality control systems, namely, the…

多项分布概率估计中的辅助性悖论AI 解读

Let X be a multinomial (n, p) variable, where n is an ancillary statistic. In Section 2, it is shown that the minimax estimator of p for fixed sample size n is not minimax for squared error loss. In Section 3, it is shown that the minimax estimator of p for fixed sample size n is still minimax for relative squared error loss.

三个正态均值多重比较检验的功效AI 解读

This article gives theoretical reasons for the findings of a simulation study by Shaffer (1981). Two well-established procedures for multiple comparison of three normal means are compared—an F procedure and an R procedure. It turns out that for a large set of parameters the average number of rejected pairwise hypotheses is larger when the F procedure is applied. To achieve our result we have to prove a special instance of a conjecture by David, Lachenbruch, and Brandis…

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基于广义 Mann–Whitney 统计量的概率置信区间与容忍区域AI 解读

Inference procedures are proposed for any specified function of two random variables f(X, Y), assuming that independent random samples from the X and Y populations are available. A generalization of the Mann-Whitney statistic is used to obtain point and interval estimates for the probability that f(X, Y) falls in a given interval. One proposed confidence interval is a modification and improvement to the approach of Halperin, Gilbert, and Lachin (1987) for estimating Pr(X <…

指数族非线性模型中正态近似准确性的诊断AI 解读

Diagnostics are investigated for assessing the agreement between likelihood and standard large-sample confidence regions for parameters from an exponential family nonlinear model (Cordeiro and Paula 1989). The development connects the contour methods proposed by Hodges (1985, 1987) with the curvature measures for normal, nonlinear regression proposed by Bates and Watts (1980) and Jennings's (1982, 1986) diagnostics for logistic regression. The proposed methodology is…

利用正交级数指数形式进行密度估计AI 解读

If a density is represented as an exponential of a series of orthogonal polynomials, it has a simple likelihood with a complete set of sufficient statistics. To ensure that the maximum likelihood equations are well conditioned, the polynomials should be orthogonal with respect to the estimated density. The optimal number of terms in the series can be determined by minimizing an estimate of a loss function. The penalized likelihood equations can be solved with little extra…

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《揭示多元异常值与杠杆点》：评论AI 解读

Detecting outliers in a multivariate point cloud is not trivial, especially when there are several outliers. The classical identification method does not always find them, because it is based on the sample mean and covariance matrix, which are themselves affected by the outliers. To avoid this masking effect, we propose to compute distances based on very robust estimates of location and covariance. In the case of regression data, the outliers also may be unmasked by using a…

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联邦福利质量控制项目中的回归估计AI 解读

States that administer federal family welfare programs review samples of the beneficiaries to guide corrective actions. Federal agencies review subsamples of the state samples to compute overpayment error rates using a regression estimator. These federal estimates make state-to-state comparisons of quality possible and are also used for fiscal sanctions. Such applications of the regression estimator have been widely challenged. We show that the regression estimates and…

评估多行观测对矩阵条件数的影响AI 解读

Given a matrix X of n observations on k variables, it is known that the singular values of X can change substantially when few rows are omitted from X. Hadi (1988) shows that no general closed-form equation can relate the singular values of X to the singular values of X with one row deleted and gives closed-form approximations to the relationship between the singular values of the two matrices. In this article, we extend Hadi's results to the more general case of…

指数分布混合假设的检验与混合分布的矩估计AI 解读

This article presents nonparametric methods for testing the hypothesis that duration data can be represented by a mixture of exponential distributions. Both Bayesian and classical tests are developed. A variety of apparently distinct models can be written in mixture of exponentials form. This raises a fundamental identification problem. A consistent estimator for the number of points of support of a discrete mixture is developed. A consistent method-of-moments estimator for…

利用 S 系统微分方程计算统计密度、累积分布、分位数与功效AI 解读

A comprehensive approach for the analysis of statistical univariate distributions is advanced. The method is based on recasting a distribution in a canonical set of first-order nonlinear differential equations called an S system, in which the derivative of each variable equals a difference of products of power-law functions. The recasting techniques are illustrated with some examples from central and noncentral probability distributions. The density and the cumulative,…

过度离散泊松回归及其他拟似然模型中的假设检验AI 解读

Test statistics for evaluating the significance of added variables in a regression equation are developed for mixed Poisson models, where the structural parameter φ that determines the mean/variance relationship var(μ; φ) = μ + φ · μ 2 is estimated by the method of moments and the regression coefficients are estimated by quasi-likelihood. The formulas presented for test statistics and related estimating equations are applicable generally to quasi-likelihood models specified…

聚类抽样下多组二乘二列联表共同优势比估计的模拟研究AI 解读

This article presents the results of a simulation study of the estimation of a common odds ratio in multiple-contingency tables when the data are correlated within clusters. The correlation is modeled by the beta-binomial distribution. The three objectives of the study were to determine (a) the variances, biases, and relative efficiencies of the beta-binomial maximum likelihood estimator (MLE), the binomial MLE, and the Mantel-Haenszel estimator of the common odds ratio; (b)…

基于单样本程序的删失生存时间中位数双样本推断AI 解读

Confidence intervals for median survival times are derived for censored survival data. The intervals are obtained by using the quantiles of the Kaplan-Meier product-limit estimator and have the same Pitman efficiency as the intervals found by inverting the sign test. Two-sample tests and confidence intervals for the difference in median survival times are then developed based on the comparison of the one-sample confidence intervals. Several methods for choosing the…

重复测量设计中区组间秩统计量的效率AI 解读

For factorial designs, tests that rely on the method of n rankings, for example, the Friedman test, suffer a potential loss of power since they depend only on within-block ranks. This deficiency is overcome by ranking across blocks as is done in the aligned rank tests and the rank transform procedures. This article examines a broad class of powerful interblock rank statistics for testing for both treatment effects and ordered alternatives and for performing multiple…