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线性混合：二元数据趋势线的新方法AI 解读

This article describes a new, biologically motivated model for bivariate data containing a trend line. The model is characterized by a mixture in which the component means lie on a line. Consistent methods for estimating the parameters of the mixture line are derived, as are procedures for obtaining a confidence interval for the slope. The methods are proved valid within a large class of models for bivariate data, including an errors-invariables model, and are illustrated…

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History Conceptual Foundations Uses and Kinds of Inference The Logic of Content Analysis Designs Unitizing Sampling Recording Data Languages Constructs for Inference Analytical Techniques The Use of Computers Reliability Validity A Practical Guide

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Clevenson–Zidek 型估计量的稳健性AI 解读

For estimating the means of several independent Poisson distributions, Clevenson and Zidek (1975) were the first to propose a class of estimators that are better than the usual one under the normalized squared error loss (1.1). This class of estimators was subsequently enlarged by others. This article examines the sensitivity of the superiority of the Clevenson-Zidek (CZ)-type means estimators over the usual one with respect to the exactness of the Poisson distribution…

论结构的本质与发现AI 解读

Extending principles of experimentation, we discuss conditions under which nonexperimental data allow consistent estimation of effects of the kind revealed by experimentation and relevant to decisions. We show how implications of these conditions are often overlooked and how failure to distinguish between “factors” and “concomitants” makes almost anything said about a model ambiguous if not wrong. The effects to be estimated dictate the factors to be included; consistency…

条件独立的 2×2×2 列联表中边际概率的假设检验AI 解读

Consider a 2 × 2 × 2 contingency model with factors A, B, and C. Assume factors A and B are conditionally independent given factor C. We are interested in testing the null hypothesis that the marginal probabilities of the second level of B are the same across the levels of A. Small-sample and large-sample tests are studied.

捕获—再捕获模型的检验、点估计与置信集AI 解读

A capture-recapture model that depends on the “catch-ability” of the individuals in a closed population is considered. A test is derived to decide if the capture efficiencies are the same for two capture attempts. The test given assumes no a priori information about the population and can be used even if one is dealing with relatively small populations. Statistical inferences are drawn about the size of the population. In particular, a family of point estimators for the…

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简单线性模型中随机游走系数检验的比较AI 解读

The locally most powerful test is derived for the hypothesis that the regression coefficients are constant over time against the alternative that they vary according to the random walk process. When the regression equation contains the constant term only, comparisons are made with the tests suggested by LaMotte and McWhorter (1978). These are based on exact powers and on three different types of asymptotic efficiencies including the classical Pitman and Bahadur approaches…

含外生变量的向量自回归移动平均模型的快速估计方法AI 解读

A very fast and simple algorithm for estimation of the parameters of large multivariate time series and distributed lag models is presented. An analysis of the distribution of the estimates shows that they are asymptotically normal and unbiased, and that they have a variance that decreases like 1/n, n being the sample size. The algorithm is especially applicable for estimation of large multivariate models where it is generally many times faster than maximalization algorithms.

样本调查中模型依赖推断与概率抽样推断的评估AI 解读

In this paper we are concerned with inferences from a sample survey to a finite population. We contrast inferences that are dependent on an assumed model with inferences based on the randomization induced by the sample selection plan. Randomization consistency for finite population estimators is defined and adopted as a requirement of probability sampling. A numerical example is examined to illustrate the dangers in the use of model-dependent estimators even when the model…

关于方差合并估计的一个说明AI 解读

The estimation of variance in the normal distribution is studied under statistical inference based on conditional specification. When there are two samples available for estimating the variance and it is not certain whether the two samples are from the same population, the experimenter usually uses a test to resolve the uncertainty. When the test is not significant, the samples are pooled to obtain a pooled estimator; otherwise, the individual sample variance is used. The…

加权回归估计值的集合AI 解读

We present in this article several results that characterize the set of all weighted regressions. The set of weighted regression estimates is the set of all generalized least squares estimates for covariance matrices that have positive weights on the diagonal and have zeroes elsewhere. The study of sets of estimates is a method for dealing with distributional uncertainty, which does not require the strong assumption of a particular distribution. We show that the set of…

一般情形下未来样本中位数的非参数预测区间AI 解读

This article deals with nonparametric prediction intervals for the median(s) of a future sample of arbitrary size without any assumption about the parent distribution. The best possible distribution-free lower bounds for the relevant coverage probabilities are derived. Furthermore, these sharp lower bounds are given in terms of lower tail probabilities of hypergeometric and binomial distributions for which extensive tables and good approximations are available.

若干简便的 t 统计量AI 解读

This article explores the use of t statistics based on two-or four-order statistics. The functions of the order statistics, which are used to define the t statistics, are the pivots and bipivots. The pivots are exact order statistics, while the bipivots are the means of two adjacent order statistics. Two t statistics, based on the pivots and bipivots, are examined and compared to other t statistics, including Student's t, under various sampling situations. We conclude that…

回归中 Scheffé 型置信界与等宽置信界的比较AI 解读

Conditions are given for when the Scheffé-type bound has smaller average width than the constant-width bound when coverage probabilities are equal, for bounding a multilinear regression function with intercept over one of the ellipsoidal regions of Halperin and Gurian (1968). The conditions depend on the size of the region relative to the design, and they are shown to hold for the special case of an orthogonal design, when the regressors are restricted to the boundary of the…

线性模型中基于秩的推断的几何解释AI 解读

Four different approaches, based on ranks, to testing hypotheses are unified through the geometry of the linear model. The various tests are identified with different but algebraically equivalent forms of the classical F test. Small sample differences are investigated via a Monte Carlo study using both rank and signed rank tests.

利用多变量辅助信息的有限总体抽样AI 解读

This article examines strategies that are approximately design-unbiased and nearly optimal, assuming a large-sample survey and a regression superpopulation model. A new class of predictors is proposed to link certain features of optimal design-unbiased and model-unbiased predictors. Generalized regression predictors are shown to pervade the subclass of asymptotically design-unbiased (ADU) predictors. Generalized regression predictors are combined with model-based…

非平稳自回归模型下的多元均值推断AI 解读

Inference about multivariate means is investigated for the case in which the covariance matrix is assumed to follow an antedependence model, which is a general first-order autoregressive model. We present two test statistics that offer alternatives to Hotelling's T 2 test for testing whether a vector mean is equal to some specified value. These antedependence statistics have simple representations in terms of Hotelling's T 2 statistics computed for certain bivariate and…

约束最小二乘回归的一种算法AI 解读

A commonly occurring problem in statistics is that of minimizing a least squares expression subject to side constraints. Here a simple iterative algorithm is presented and shown to converge to the desired solution. Several examples are presented, including finding the closest concave (convex) function to a set of points and other general quadratic programming problems. The dual problem to the basic problem is also discussed and a solution for it is given in terms of the…