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利用狄利克雷混合分布估计二乘二列联表的贝叶斯方法AI 解读

In the estimation of cell probabilities from a 2 × 2 table, a prior distribution is developed that can reflect prior beliefs about the cross-classification structure in the table. The posterior means using this prior shrink the classical estimates towards the association structure specified a priori by the user. Closed-form approximations to the posterior means and credible regions are developed in the special case where the two variables of the table are believed…

广义条件下回归函数核估计的一致收敛AI 解读

In this article we prove uniform consistency of kernel estimators of a multivariate regression function under various assumptions on the distribution of the data. In addition to the usual assumptions that the data are iid and that the distribution of the regressors is absolutely continuous, we consider the cases that some regressors are discrete and the data are either stationary ϕ-mixing themselves or generated by a class of functions of one-sided infinite stationary…

多元正态分布均值的经验贝叶斯置信集AI 解读

Through the use of an empirical Bayes argument, a confidence set for the mean of a multivariate normal distribution is derived. The set is a recentered sphere, is easy to compute, and has uniformly smaller volume than the usual confidence set. An exact formula for the coverage probability is derived, and numerical evidence is presented which shows that the empirical Bayes set uniformly dominates the usual set in coverage probability.

判别分析中的随机效应模型AI 解读

In this article the characteristics of classical discriminant analysis under the random-effects model are investigated. Assuming that the elements within any randomly selected population are normally distributed with mean vector μ and common covariance matrix Σ, and that over different populations μ has a normal distribution with mean vector ξ and covariance matrix T, the distribution of the population-based and sample-based Mahalanobis distances between two different…

双向布局中的分布无关秩检验AI 解读

A class of distribution-free statistics using scores based on ranks for testing main effects in two-way layouts, with no interactions and more than one observation per cell, is discussed. Asymptotic distributions are developed under the null and alternative hypotheses for the case in which cell size is fixed and the number of blocks is allowed to become large, and as cell size becomes large with the number of blocks fixed. Efficiencies are considered under both asymptotic…

总体分布长尾时，t 检验真的保守吗？AI 解读

It is generally believed that the t test is conservative for a sample from a long-tailed symmetric distribution. Yet the probability inequalities expressing this property have not been proved. The inequalities are explored here using various criteria for long-tailedness and leaning on the geometrical interpretation of the t test. It is proved that the t test is conservative but only for large enough critical values. Examples of a liberal t test for lower values are given.…

区间上简单线性回归的精确置信带AI 解读

Exact simultaneous confidence intervals and bands for the regression line on a set Cx in simple linear regression have been known only when Cx is a finite set with one or two points or when Cx is a finite or infinite interval. Otherwise, conservative bands have been used. In this article we present a method for constructing exact confidence bands on an arbitrary finite union of intervals or points. Also, tables are provided for cases of finite Cx with three points and of Cx…

多重超几何函数的概率解释与统计用途AI 解读

This article reviews and interprets recent mathematics of special functions, with emphasis on integral representations of multiple hypergeometric functions. B.C. Carlson's centrally important parameterized functions R and ℛ, initially defined as Dirichlet averages, are expressed as probability-generating functions of mixed multinomial distributions. Various nested families generalizing the Dirichlet distributions are developed for Bayesian inference in multinomial sampling…

线性贝叶斯估计量的一般方差修正AI 解读

We consider the problem of modifying the linear Bayes estimator for the mean of a distribution of unknown form by using an estimate of sample variance. The general conditions under which there is no advantageous variance modification to the linear Bayes rule are identified. These results are applied to the problem of sampling from a normal distribution with unknown mean and variance, and the implications are discussed.

涂抹估计：一种非参数逆变换方法AI 解读

The smearing estimate is proposed as a nonparametric estimate of the expected response on the untransformed scale after fitting a linear regression model on a transformed scale. The estimate is consistent under mild regularity conditions, and usually attains high efficiency relative to parametric estimates. It can be viewed as a low-premium insurance policy against departures from parametric distributional assumptions. A real-world example of predicting medical expenditures…

含日历变动的时间序列建模AI 解读

The modeling of time series data that include calendar variation is considered. Autocorrelation, trends, and seasonality are modeled by ARIMA models. Trading day variation and Easter holiday variation are modeled by regression-type models. The overall model is a sum of ARIMA and regression models. Methods of identification, estimation, inference, and diagnostic checking are discussed. The ideas are illustrated through actual examples.

不完整配对观测下的可互换性检验AI 解读

A class of conditionally distribution-free rank order tests is developed for testing interchangeability of two correlated variates with incomplete data on both responses. Asymptotic properties of these tests are examined. In particular, we show that the proposed tests are also asymptotically distribution-free. For location alternatives, the Pitman efficiency of the rank order test relative to the parametric test based on the bivariate normal model is investigated.

考虑二分子组选择的 P 值调整AI 解读

Using a probability inequality, we show that if U = ([Udot], Ü), [Udot] = (U 1, …, U k), Ü = (U k + 1, …, U 2k ) has a multivariate normal distribution with mean vector zero and covariance matrices cov([Udot], [Udot]) = cov(Ü, Ü) = R, cov([Udot], Ü) = e'e – R, where R is a k × k correlation matrix and e = (1, …, 1), then P{|U 1| < c, …, |U 2k | < c} is minimized by setting all correlations in R equal to ½. This result is used to adjust the apparent significance of a…

删失数据下双参数递减风险率分布的最大似然估计AI 解读

Problems of maximum likelihood estimation are discussed for shape and scale parameters from certain decreasing hazard rate distributions, typically either mixed-exponential or “work-hardened.” Sufficient conditions on the mixing distribution are given that guarantee regular behavior of the hazard rate and that ensure, even with highly censored data, that the MLE's exist from such DHR distributions whenever the sample satisfies a certain condition; otherwise a constant hazard…

信息不足时的估计AI 解读

As a possible explanation for the existence of absurd UMVU estimators, a class of estimation problems is defined: estimating the probability of an “unobservable” event, for example, estimating the probability of an event of interest occurring over a long period of time from observations over a much shorter period. It is pointed out that in typical cases of this kind, no reasonable unbiased estimator can exist. Consideration of the maximum likelihood estimator suggests the…

无偏性作为贝叶斯性的对偶AI 解读

In this note we define the notion of unbiasedness for a decision function for an arbitrary loss function. This is a generalization of Lehmann's (1951) definition. We show that this notion of unbiasedness is a dual to the notion of being Bayes; that is, if the role of the random variable and the parameter is interchanged, then unbiasedness is equivalent to being Bayes and vice versa. Some consequences of this fact are discussed.

面向使用者的统计推断AI 解读

A class of inferential procedures (called user-oriented procedures) related to the equal probability test of Arrow (1960) is introduced for use in many univariate problems. These procedures require that experimenters be able to interpret the parameters about which they wish to make inference. The class of procedures include confidence intervals associated with the equal probability test as well as an analogue to the P value. The confidence intervals are easier to interpret…

不等概率抽样下的有限总体均值估计AI 解读

Two approaches to estimating a finite population mean from unequal probability samples are contrasted. In the prediction approach a model is specified for the population values and is used to predict the nonsampled values. In the generalized regression approach the Horvitz-Thompson estimator of the population mean is modified to allow the introduction of covariate information (Särndal 1980). Generalized regression estimates have the desirable property of asymptotic design…

为多元一般线性形式生成特征可控的测试数据AI 解读

Experiments to assess the performance characteristics, both of statistical methods and of computer programs that implement them, are best performed using test data with controlled statistical and numerical properties. We describe an algorithm for constructing test data for any multivariate linear model that provides complete control (subject only to the requirement of mutual consistency) over the following factors: regression coefficients; regression and residual sums of…

死刑案件陪审团：一项法律程序的统计分析AI 解读

Potential jurors in capital cases are often queried on their attitudes toward capital punishment. The extreme groups say they would never or they would always approve capital punishment, given a guilty verdict. In many jurisdictions, these two groups are routinely excluded from juries deciding whether the defendant is guilty in capital cases. This exclusion persists even when the potential jurors say they could be fair and impartial in deciding guilt or innocence. The…

分层样本多元回归中调查权重的使用AI 解读

The rationale for the use of sample survey weights in a least squares regression analysis is examined with respect to four increasingly general specifications of the population regression model. The appropriateness of the weighted regression estimate depends on which model is chosen. A proposal is made to use the difference between the weighted and unweighted estimates as an aid in choosing the appropriate model and hence the appropriate estimator. When applied to an…

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