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稳定分布参数的回归型估计AI 解读

A regression-type method of estimating the four parameters of a stable distribution is presented. The estimators found are consistent and approximately unbiased for moderately large sample sizes. Their efficiencies, found through a simulation study, are greater than those of most other estimators for large portions of the parameter space. Moreover, the amount of computation involved is minimal and apparently less than that needed by the methods of Paulson, Holcomb, and…

将线性估计外推至更大样本量AI 解读

A study is performed of McCool's method for constructing linear estimates from order statistics when the coefficients of a linear estimate for a smaller sample size are available. The efficiency of the method is investigated, using the theory of U statistics. Among other things, it is shown that in the case of the logistic distribution, the method produces an asymptotically efficient location parameter estimate and, in the case of the Pareto distribution, an asymptotically…

通过提名抽样估计总体中位数AI 解读

In nomination sampling, the largest values from several independent random samples (nominees) are rank ordered, and an estimate of the population median is formed by interpolating between 2 of these order statistics. The resulting estimate compares favorably to the sample median of a simple random sample from the same population. When historical data sets retain only extreme values, nomination sampling may offer the only practical way to estimate the population median. The…

线性回归中线性后验期望对正态分布的刻画AI 解读

We consider the general linear model Y = Aβ + ε in the Bayesian framework and examine the implications of the statement that the posterior expectation of β, given Y, is a linear function of Y. Under various conditions on the model, it is shown that this linear posterior expectation implies that both β and ε are normally distributed. For most of the practical situations in which linear models are used, only normal distributions have linear posterior expectations.

普通线性模型与复相关模型中 F 检验的渐近有效性AI 解读

In this article we establish under fairly general conditions that the F tests used in the linear model and the correlation model are asymptotically valid in the presence of nonnormality, in that their sizes are unaffected, asymptotically, by this nonnormality. Similar results could be derived for Scheffé-type simultaneous confidence intervals as well as the one-sided t tests used in these models. Finally, we find the asymptotic distribution of the sample variance and show…

协方差分析中的多重比较程序AI 解读

Currently available range-type procedures for constructing simultaneous confidence intervals on contrasts in analysis of covariance (ANCOVA) models with random covariates assume that the vectors of covariates associated with the observations are identically distributed. Conditions are given under which the mean vectors of these covariates may differ without affecting the validity of such procedures. An example of a controlled test market experiment illustrates the usefulness…

方差非负线性组合的置信区间AI 解读

Smith (1936) suggested a method that can be used for setting confidence limits on linear combinations of variances. This method was studied and expanded by Satterthwaite (1941, 1946) and has become known as Satterthwaite's procedure. The procedure has been widely used for the past 40 years. In this article a new procedure is proposed for this problem that is better than Satterthwaite's procedure and very easy to compute from existing tables.

构造具有可控特征的回归：探查回归表现的方法AI 解读

Studies of robust regression algorithms have generally relied on Monte Carlo trials and have concentrated on evaluating the algorithm's performance for long-tailed error distributions. This article identifies other aspects of data structure that can influence the performance of robust regression procedures and presents an algorithm for constructing regression problems in which each of these factors can be controlled separately. The method generalizes to multiple regression…

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实例回归分析AI 解读

Simple Linear Regression Multiple Linear Regression Regression Diagnostics: Detection of Model Violations Qualitative Variables as Predictors Transformation of Variables Weighted Least Squares The Problem of Correlated Errors Analysis of Collinear Data Biased Estimation of Regression Coefficients Variable Selection Procedures Logistic Regression Appendix References Index.

计数数据的趋势检验：多项分布情形AI 解读

Given k multinomial probabilities pi (Σ pi = 1), let pi be a known continuous function f (wi, πi ) of a known weight constant wi and an unknown constant π i . The function f is assumed strictly monotone in π. The maximin statistic for testing the homogeneity of the π i 's versus a trend in the π i 's is derived. The Armitage statistic for testing linear trend is maximin for a certain alternative hypothesis space. The methods are applied to lying habit data (Maxwell 1961),…

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基于预先显著性检验的回归型估计量AI 解读

If data on an auxiliary variable X correlated with the variable Y under study are available, regression-type estimators are often used to estimate the population mean μ y . An estimator based on a preliminary test of significance that chooses between the difference estimator and the regression estimator has been proposed. This article investigates the efficiency of the proposed regression-type estimator with respect to other regression-type estimators.

将线性估计外推至更大样本量AI 解读

A study is performed of McCool's method for constructing linear estimates from order statistics when the coefficients of a linear estimate for a smaller sample size are available. The efficiency of the method is investigated, using the theory of U statistics. Among other things, it is shown that in the case of the logistic distribution, the method produces an asymptotically efficient location parameter estimate and, in the case of the Pareto distribution, an asymptotically…

线性回归中线性后验期望对正态分布的刻画AI 解读

We consider the general linear model Y = Aβ + ε in the Bayesian framework and examine the implications of the statement that the posterior expectation of β, given Y, is a linear function of Y. Under various conditions on the model, it is shown that this linear posterior expectation implies that both β and ε are normally distributed. For most of the practical situations in which linear models are used, only normal distributions have linear posterior expectations.

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构造具有可控特征的回归问题：考察回归性能的方法AI 解读

Studies of robust regression algorithms have generally relied on Monte Carlo trials and have concentrated on evaluating the algorithm's performance for long-tailed error distributions. This article identifies other aspects of data structure that can influence the performance of robust regression procedures and presents an algorithm for constructing regression problems in which each of these factors can be controlled separately. The method generalizes to multiple regression…

两组多重时间序列共同群延迟的估计AI 解读

The group delay at frequency λ between two univariate time series represents the time lag of the harmonic component at frequency λ of the first series behind the corresponding harmonic component of the second series. This article proposes an estimate of group delay under conditions that arise in dendrochronology where each of A tree ring time series shares a common group delay with each of B other tree ring time series and where the common group delay is constant over a…

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随机化回答设计的线性模型AI 解读

Linear models, based on random permutation models, are developed to include a wide class of one-sample randomized response designs. The general form of the “optimal” estimator of the finite population mean or proportion is obtained. Most of the conventional randomized response estimators are seen to be optimal, in terms of minimum average mean squared error, within their associated designs. The optimality results are obtained for sampling without replacement and include…