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已知方差的若干多元正态模型中相关系数的简易最优渐近正态估计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…

方差分量的非负估计与预检验估计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.

医学试验中的随机化“胜者续用”规则AI 解读

In a sequential medical trial, a simple randomized treatment assignment rule is proposed and analyzed. On the average this rule assigns more patients to the better treatment, and it is applicable to the case where patients have delayed responses to treatments. This new assignment rule is studied for both a fixed sample size and an inverse stopping rule.

Logistic模型与潜在结构的估计AI 解读

Consider the logistic model for dichotomous response involving a group of individuals with varying levels of ability and a set of items with varying degrees of difficulty. This article is concerned with estimating the parameters of the latent ability distribution for any given group of individuals. An iterative procedure for obtaining maximum likelihood estimates of these parameters based on the missing information principle is presented and illustrated with real data. The…

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正态混合分布与转换回归的估计AI 解读

Since the likelihood function corresponding to finite mixtures of normal distributions is unbounded, maximum likelihood estimation may break down in practice. The article introduces the “moment generating function estimator” defined as the estimator which minimizes the sum of squares of differences between the theoretical and sample moment generating functions. The consistency and asymptotic normality of the estimator are proved and its finite sample behavior is compared to…

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…

Logistic回归与判别分析之间的选择AI 解读

Classifying an observation into one of several populations is discriminant analysis, or classification. Relating qualitative variables to other variables through a logistic cdf functional form is logistic regression. Estimators generated for one of these problems are often used in the other. If the populations are normal with identical covariance matrices, discriminant analysis estimators are preferred to logistic regression estimators for the discriminant analysis problem.…

不平衡设计中多重比较 T 方法扩展的改进AI 解读

Some improvements and clarifications of extended T-type procedures of multiple comparisons for unbalanced designs are given. In view of the general discussion, we obtain a procedure particularly tailored for one-way layouts with only two different sample sizes. In all such designs, the given procedure yields confidence intervals which are not longer than those obtained by Spjøtvoll and Stoline's (1973) method for all pairwise comparisons and are strictly shorter for some of…

扰动较小时有限信息极大似然估计量的改进AI 解读

The limited information maximum likelihood (LIML) estimator is shown to be inadmissible in terms of asymptotic expansions of the distributions of the estimators. The LIML estimator is improved by combining it linearly with the two-stage or the ordinary least squares estimator.

配对比较中的处理对比：大样本结果、应用与若干最优设计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…

线性回归模型中随机游走系数存在性的精确检验AI 解读

Exact tests of the hypothesis that the mean vector of an observed T-variate random variable follows a conventional fixed-coefficient linear model, against the alternative that the regression parameters vary according to a first-order Markov process, are derived. Power functions of the tests are investigated in order to provide means of choosing a test.

基于最大 k 个观测值的参数与极高分位数估计AI 解读

We consider an estimation problem when only the k largest observations of a sample of size n are available. It is assumed that the underlying distribution function F belongs to the domain of attraction of a known extreme-value distribution and that k remains fixed as n → ∞. We present estimators for the location and scale parameters and for p-quantiles of F, where p is of the form 1 — c/n (c fixed). These estimators are either asymptotically maximum likelihood or minimum…

混合分布的非参数极大似然估计AI 解读

The nonparametric maximum likelihood estimate of a mixing distribution is shown to be self-consistent, a property which characterizes the nonparametric maximum likelihood estimate of a distribution function in incomplete data problems. Under various conditions the estimate is a step function, with a finite number of steps. Its computation is illustrated with a small example.

基于洛伦兹曲线的无尺度指数分布拟合优度检验AI 解读

The sample Lorenz curve provides a powerful, easily computed goodness-of-fit test for exponentiality which does not depend on the unknown scale parameter. Exact critical values and asymptotic results are given, which can also be used to test the related hypothesis of randomness on an interval. General limit theorems show that the sample Lorenz curve converges almost surely to the population Lorenz curve and that the standardized Lorenz statistic converges to normality…

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…

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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.

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…

消费者购买面板数据分析的广义复合泊松模型AI 解读

A compound Poisson distribution, the Ehrenberg NBD model, has proven useful in the past for analyzing consumer purchase behavior encountered in dealing with frequently purchased low-cost consumer items. The present article proposes the use of a generalized negative binomial distribution in which the NBD model is used as a purchase occasion component and is combined explicitly with the conditional distributions of the single-purchase volume variables associated with the…

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稳健统计程序AI 解读

Background - Why Robust Procedures? Qualitative and Quantitative Robustness, Qualitative Robustness, Quantitative Robustness, Breakdown, Infinitesimal Robustness, Influence Function M-L and R-Estimates, L-Estimates, R-Estimates, Asymptotic Properties of M-Estimates, Asymptotically Efficient M-L, R-Estimates, Scaling Question Asymptotic Minimax Theory, Minimax Asymptotic Bias, Minimax Asymptotic Variance Multiparameter Problems, Generalities, Regression, Robust Covariances -…

小扰动情形下有限信息最大似然估计量的改进AI 解读

The limited information maximum likelihood (LIML) estimator is shown to be inadmissible in terms of asymptotic expansions of the distributions of the estimators. The LIML estimator is improved by combining it linearly with the two-stage or the ordinary least squares estimator.