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方差分量的非负估计量与预检验估计量AI 解读

Nonnegative estimators of variance components involving preliminary tests are studied. The restricted maximum likelihood estimator and other truncated estimators may be viewed as preliminary test estimators. A new preliminary test estimator is proposed and studied. Recommendations of the levels of preliminary tests are made.

成对比较中的处理对比：大样本结果、应用与部分最优设计AI 解读

Treatment contrasts in paired comparison experiments are considered. Given that specified orthonormal treatment contrasts are null, remaining treatment parameters, orthonormal contrasts among them, and their logarithms are estimated. The estimators are shown to be consistent and, when suitably scaled and centered, to have distribution functions that are normal in the limit for large sample sizes. Hypothesis tests on treatment contrasts are obtained. The limiting distribution…

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典型分析：比较有限离散分布函数的因子分析方法AI 解读

The methods of factor analysis are adapted to the comparison of finite discrete distribution functions. Each element of a finite class of distribution functions is presented in a canonical form in which components differentiating and uniting the functions are easily distinguished and are readily calculated using factor-analysis algorithms. This technique, which we call canonical analysis, has uses in heterogeneity and goodness-of-fit analysis and in the classification of…

小期望频数列联表的尾部概率AI 解读

In most cases where an application of the χ2 test for contingency tables is recommended, only the size of the expected values is taken into account and not the level of significance. In the present article, a method is proposed which is mainly suitable for those cases for which the applicability of the χ2 test is doubtful, whereas the exact test would require too much computational work.

多重共线性下联立方程估计量的小样本性质AI 解读

A Monte Carlo simulation is employed to reinvestigate the general disagreement in the literature regarding the small-sample properties of simultaneous equation estimators under widely different levels of multicollinearity. This disagreement has been attributed to the greater use by more complex estimators of information on variables excluded from each equation, producing the advantage in inference of increasing precision at low levels of collinearity, but the disadvantage of…

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若干已知方差多元正态模型中相关系数的简便最优渐近正态估计AI 解读

It is well-known that in certain multivariate normal models with known variances, maximum likelihood estimation of correlations is arithmetically cumbersome. For certain of these models, a relatively simple estimation technique based on the sufficient statistics is given and shown to be best asymptotically normal. The procedure uses the fact that many of the likelihood equations for these models are essentially cubic equations. A consistent, explicit solution for the…

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Smear-and-Sweep 分析中的偏差问题AI 解读

The usefulness of the smear-and-sweep technique as developed in The National Halothane Study is questioned because of greater-than-expected bias. The Halothane study took into account the bias inherent in smear-and-sweep, and an example was given to suggest that any remaining bias could be eliminated by an extension of the technique. However, a close reexamination of the example shows that a high degree of bias may remain. Another example is given to show that the bias does…

多条回归线平行性秩得分检验的小样本比较AI 解读

The small-sample behavior of rank score tests due to Adichie and to Sen is compared to the classical parametric F test for parallelism of regression lines. Empirical power functions generated by a series of Monte Carlo simulations reveal that the nonparametric tests are consistently conservative relative to the classical test and suggest that, within the confines of the experimental distributions, the parametric test is the preferred small-sample test for parallelism.

线性判别分类后一组观测的总体均值估计AI 解读

Suppose that a group of observations is known to have come from either one of two normal populations with unknown means and common variance. After the group is classified by the linear discriminant function, it is pooled with the sample from the population to which it belongs to estimate the unknown mean. Weighted estimators of the population means are defined. The biases and mean squared errors of the estimators in the univariate case are obtained. Estimators of the…

检测均值系统性变化的二变量检验AI 解读

Let (xi, yi ), i = 1, …, n, be a sequence of observations such that yi = bi + cxi + ui , where bi and c are unknown parameters, and {ui } and {xi } are independent sequences of independent, identically distributed random variables. The likelihood ratio test is derived for the hypothesis that bi = b (i = 1, …, n), against the alternative that bi = b (i ≤ i 0) and bi = b + d (i > i 0) for some b, i 0, and d ≠ 0, assuming the ui 's are normal. Quantiles of the test statistic…

嵌套分类中方差分量线性组合的精确置信区间AI 解读

Methodology is proposed for the construction of exact confidence intervals on nonnegative linear combinations of variance components from nested classification models. Examples are given for the one-fold and two-fold classifications. The robustness of these confidence intervals to model breakdown is also discussed.

简单线性回归的加权秩统计量AI 解读

This article is concerned with statistical inferences for the slope parameter β in the simple linear regression model. Rank procedures are proposed which extend the procedures of Theil and Sen by using weights for the pairwise slopes. Estimation, confidence interval, and hypothesis testing problems are considered.

极小极大自适应广义岭回归估计量AI 解读

We consider the problem of estimating the vector of regression coefficients of a linear model using generalized ridge regression estimators where the ridge constant is chosen on the basis of the data. For general quadratic loss we produce such estimators whose risk function dominates that of the least squares procedure provided the number of regressors is at least three. We study the problem by the usual reduction to estimating the mean vector of a multivariate normal…

修正二项模型下的 Dorfman 型群组检测AI 解读

In this article we introduce a new group-testing model which we refer to as the modified binomial model. This new model, when applicable, not only requires a smaller per unit expected number of tests to identify all units (in a population of dichotomous units) than does the frequently considered binomial model, but also is always preferable to individual testing. We consider optimal Dorfman-type procedures under the modified model and present methods for determining the best…

回归选择策略与显露的先验AI 解读

The computation and selection of constrained regressions may be motivated by prior information and, if so, a regression selection strategy reveals the implicit prior. The selection strategies of principal component regression, stepwise regression, and imposing equality constraints are connected with prior densities which are uniform on spheres, hyperbolas, and cones, respectively. Omitting variables in a predetermined order reveals lexicographic priors.

线性不等式约束下线性模型的贝叶斯分析AI 解读

This article considers the general linear model when the parameter space is subject to linear inequality constraints. A Bayesian analysis of this model is presented using a natural conjugate prior of the mixed type. Expressions are given for the probability that constraints are binding and for the distribution of the parameters. When prior information about the parameters is vague, the Bayesian and sampling methods of model selection are compared. The techniques are applied…

使用稳健估计的广义线性与二次判别函数AI 解读

Two new methods of constructing robust linear and quadratic discriminant functions are introduced. The first is a generalization of Fisher's procedure for finding a linear discriminant function. It places less weight on those observations that are far from the overlapping regions of the two populations. The second new method substitutes M-estimates of the means and the covariance matrices into the usual expressions for the linear and quadratic discriminant functions. Monte…

数据收集前聚合问题的决策理论方法AI 解读

We present a decision-theoretic approach to finding optimal aggregation schemes when the aggregation is made at the pre-data-collection stage. A criterion is presented for the optimal aggregation of variables, its properties are analyzed, and it is compared with other criteria in the literature for good aggregation. In the course of determining this criterion, we derive endogenously the disaggregation procedure by which inferences about disaggregated data are made from…

非对称总体的修正 t 检验与置信区间AI 解读

This article considers a procedure that reduces the effect of population skewness on the distribution of the t variable so that tests about the mean can be more correctly computed. A modification of the t variable is obtained that is useful for distributions with skewness as severe as that of the exponential distribution. The procedure is generalized and applied to the jackknife t variable for a class of statistics with moments similar to those of the sample mean. Tests of…

百分位数回归：参数化方法AI 解读

For situations in which no assumptions are explicitly made about error distributions, other model assumptions may imply constraints on the form of the residual distribution. This is true of regression models which assume that percentiles are functions of the regressor variable. Hogg (1975) used a procedure based on signs of residuals to fit linear percentile models. Advantages of making (and testing!) explicit parametric assumptions in this context are illustrated using a…