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信息度量与贝叶斯层级模型AI 解读

We consider the Bayesian statistical models in which the prior distribution of the parameter vector θ1 in the distribution of an observable random vector X is to be specified in a hierarchical fashion and one wants to learn about the hyperparameters at each level of this prior distribution. It is shown that for a wide class of information measures, based on the so-called f divergence, the information decreases as one moves to higher levels of hyperparameters. This result…

Hunter同时推断方法及其在已知高相关结构中的应用AI 解读

The Hunter (H) method of simultaneous estimation of all means is based on a second-order Bonferroni-type inequality and is superior to the Bonferroni (B) method. This method is applicable for cases using a multivariate t distribution with correlation matrix R = (ρ ij ) and is shown to be decidedly superior to the B method when the correlations ρ ij in R are all large (|ρij| > .5). This article presents an example, using data from Draper and Smith (1966), in which the 95…

自回归误差回归模型预测的小样本性质AI 解读

Monte Carlo methods are used to examine the small-sample properties of various estimators of asymptotic prediction variance (APV) from the regression model with autoregressive errors. Two practical estimators of APV, one of which includes terms reflecting parameter estimation and one of which excludes these terms, are compared to the mean squared error of prediction for regression models with different autocorrelation of the errors, different sample sizes, and different…

儿童死亡后的生育反应：一个最大似然估计模型AI 解读

The individual household's fertility response to an experienced child death, the replacement probability, is estimated for Brazil using a maximum likelihood estimation model. This model, which treats births, deaths, and replacement births as endogenous and which assumes discrete distributions for these random variables, avoids the statistical problems of earlier estimates. The model allows the distribution of births, deaths, and replacement births to vary with included…

临床化学中污染正态分布的一种估计程序AI 解读

Mixtures of normal distributions have been used in modeling a wide variety of experimental data in fields as different as fisheries biology and medicine. A problem in the field of nutrition concerning estimation of the population proportion of anemic individuals from a sample of hemoglobin values has led to consideration of a class of mixtures of two components, where only the predominant component is assumed to be normal. The second component is assumed to contaminate only…

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密度估计修正似然的一则注记AI 解读

Let f λ be a kernel estimate (with window width λ) of the density f. Its performance is assessed by the Kullback-Leibler information distance I(f, f λ) = ∫ f log f − ∫ f log f λ. This article establishes conditions for the asymptotic equivalence of the cross-validation estimate and the jackknife estimate of the term ∫ f log f λ, and provides the common limiting value. This gives insight into the “modified likelihood” criterion for choosing λ, introduced by Habbema, Hermans,…

二项分布似然函数的单峰性AI 解读

A maximum likelihood estimate exists for both parameters of the binomial distribution if and only if the sample mean exceeds the sample variance. The derivative of the log-likelihood function has at most one finite root; consequently the likelihood function is unimodular.

确定时间序列周期的一种方法AI 解读

The periods corresponding to peaks in the autoregressive and window spectral density estimators are shown to be consistent and asymptotically normal estimators of peak periods in the true spectral density under assumptions of known autoregressive order and under slight modifications of the assumptions often made to show the asymptotic normality of window estimators, respectively. The asymptotic variances are obtained, and the use of the theory is illustrated by obtaining an…

指数族多峰分布的估计与矩递推关系AI 解读

Multimodal generalizations of the normal, gamma, inverse gamma, and beta distributions are introduced within a unified framework. These multimodal distributions, belonging to the exponential family, require fewer parameters than corresponding mixture densities and have unique maximum likelihood estimators. Simple moment recursion relations, which make maximum likelihood estimation feasible, also yield easily computed estimators that themselves are shown to be consistent and…

位置尺度剂量反应曲线中位置参数的小样本二元反应估计AI 解读

When one uses a small number of quantal responses to estimate a location parameter in the presence of an unknown scale parameter for a logistic or normal dose-response curve, it is often possible to substantially improve upon the method of maximum likelihood. Some generalized method-of-moments estimators are proposed for an arbitrary dose-response curve known up to location and scale and a theorem is given that establishes existence and uniqueness properties. In a computer…

非线性回归与样条平滑的信号提取方法AI 解读

This article shows how to fit a smooth curve (polynomial spline) to pairs of data values (yi, xi ). Prior specification of a parametric functional form for the curve is not required. The resulting curve can be used to describe the pattern of the data, and to predict unknown values of y given x. Both point and interval estimates are produced. The method is easy to use, and the computational requirements are modest, even for large sample sizes. Our method is based on maximum…

利用非随机处理分配：犯罪控制项目的断点回归评估AI 解读

Despite the enormous potential of regression-discontinuity, quasi-experimental procedures, they have to date rarely been used in the evaluation of large-scale social programs. In this article, we report an evaluation of such a program in which a regression-discontinuity analysis is employed. Through a change in legislation, the program in question extended eligibility for unemployment benefits to prisoners after their release from prison. The regression-discontinuity…

合并列联表中 Pearson 卡方统计量的可分解性、单调性及应用AI 解读

The Pearson chi-square statistic for a contingency table is decomposed into a sum of components. Each component involves the Pearson chi-square statistic for tables that are formed by collapsing (i.e., combining) rows and/or columns of the original table. Since the terms in the decomposition are necessarily nonnegative, this leads to a monotonicity in the statistic; the Pearson chi-square value for any table N is never smaller than the corresponding values for tables formed…

回归模型的得分检验AI 解读

Many score statistics used for testing trends in means, either based on the observed values of the response variables or their ranks, can be expressed in terms of quadratic forms. This article explores systematically the robustness of optimality of these statistics, as well as the optimal properties of the associated tests.

从预测视角识别与刻画回归中的影响观测AI 解读

Assuming a set of observations is available from the general linear model, and assuming prior information about parameters, we propose a method of assessing the influence of specified subsets of the data when the goal is to predict future observations.

回归方程应纳入多少个变量？AI 解读

The optimal number of regressors is determined to minimize mean squared prediction error and is shown to be a small fraction of the number of data points. As the number of regressors grows large, the Sp criterion provides an asymptotically optimal rule for the number of variables to enter.

利用辅助信息进行方差估计AI 解读

Variance estimators under several sample designs are proposed and compared when auxiliary information is available. Improvement of the bias and mean squared error over some estimators commonly used in practice is illustrated. A Monte Carlo comparison of the estimators is also presented.

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二元数据的实验设计AI 解读

Models for binary data are usually such that the information matrix depends on the unknown parameters. Thus the standard criteria for optimality in regression experiments cannot be applied without modification. Methods of going around this difficulty include the use of initial point estimates, sequential methods, and Bayesian analysis. This article is mainly concerned with the robustness and the number of design points for methods involving initial estimates, and for…

有界影响回归的极小极大性质AI 解读

Bounded-influence regression (in the sense of Hampel-Mallows-Krasker-Welsch) is examined critically from the point of view of finite-sample minimax robust estimation theory. The main conclusion is that the influence of position of very high leverage points—that is, of points where the diagonal element of the hat matrix H = X(XTX)−1 XT exceeds a certain bound—should be cut down selectively. This bound should be chosen roughly between .2 and .5; for the upper of these values,…

参数经验贝叶斯推断：理论与应用AI 解读

This article reviews the state of multiparameter shrinkage estimators with emphasis on the empirical Bayes viewpoint, particularly in the case of parametric prior distributions. Some successful applications of major importance are considered. Recent results concerning estimates of error and confidence intervals are described and illustrated with data.

“真实”时间序列及其指标AI 解读

A problem that economic statisticians frequently face is to estimate the true movement in a time series on the basis of two or more imperfect indicators. A well-known example is nonagricultural employment as indicated (a) by a monthly survey of households and (b) by a monthly survey of employers. This article describes a procedure for estimating true changes in a time series as a linear combination of two indicators, with weights for indicators chosen so as to minimize…