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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),…

两个相关 t 随机变量乘积的分布AI 解读

Two forms of the distribution function of the product of two correlated t variates are presented. The distribution function is studied as a function of three parameters.

基于排序集样本的二元正态总体相关系数推断AI 解读

Ranked set sampling was first used to obtain an improved estimate of a population mean. This technique is useful when a small random sample can be visually ordered easily and fairly accurately, but exact measurement of an observation is difficult or expensive. The sampling method is generalized and applied to estimation of the correlation coefficient ρ of a bivariate normal random vector (X, Y). The asymptotic variance of the maximum likelihood estimator of ρ based only on…

多元正态总体均值的序贯估计AI 解读

This article is a multivariate generalization of the sequential sampling procedure developed by Robbins (1959) and extended by Starr (1966b) for estimating the mean of a normal population when the scale parameter is unknown. The exact distribution of the stopping time is derived for the sequential procedure, and a recursive method for computing the distribution of the stopping time is proposed that can be easily programmed for mechanical calculation. It is shown that the…

一类二次损失函数下的多元正态均值估计AI 解读

Stein's estimator for p ≧ 3 normal means is known to dominate the usual estimator if the loss is quadratic. Brown (1975) has shown that for a class of quadratic loss functions the usual estimator can be uniformly improved if the loss functions do not give such extreme weights to the coordinates that the problem essentially reduces to a two-dimensional one. However, he has not given a uniformly better estimator. In this article, we give explicit alternatives that uniformly…

线性递归方程、协方差选择与路径分析AI 解读

By defining a reducible zero pattern and by using the concept of multiplicative models, we relate linear recursive equations that have been introduced by econometrician Herman Wold (1954) and path analysis as it was proposed by geneticist Sewall Wright (1923) to the statistical theory of covariance selection formulated by Arthur Dempster (1972). We show that a reducible zero pattern is the condition under which parameters as well as least squares estimates in recursive…

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.

不完整数据下期望意义的新优于旧检验AI 解读

This article proposes a test for the problem of testing that a life distribution is an exponential distribution against the alternative that it is new better than used in expectation, not exponential, on the basis of randomly right censored data. The test statistic is an analog of the “total time on test” test statistic.

双因素方差分析中主效应的 Friedman 型秩检验AI 解读

A distribution-free test is considered for testing main effects in a two-factor ANOVA. Large-sample properties (cell sizes tending to infinity) including efficiencies and the limiting distribution of the test statistic are obtained. For proportional frequencies a simple sum of squares formula is obtained for the test statistic and multiple comparison procedures are given. For general designs the statistic is expressed using generalized inverses. Some tables for the null…

提高负二项分布与 Neyman A 型分布拟合检验功效的方法AI 解读

A modification of the quadratic form involved in a generalized minimum chi-squared procedure yields the same asymptotic null distribution of the test statistic for testing fit by an assumed model, but a different form of nonnull distribution emerges. This result is applied to testing fit of the negative binomial and Neyman Type A distributions, and tables of asymptotic power are presented that show the increase of power obtained. A numerical example is presented to…

预测变量范围受限时的线性回归置信带AI 解读

The classic procedure for constructing a confidence band around a regression function is that of Scheffé (1959), which provides a band of infinite length. This band can be unnecessarily wide if the region of interest to the experimenter is finite. A class of sets is defined that restricts the range of the predictor variables. Confidence bands for a regression function over are constructed, which, for fixed α, are narrower than the Scheffé bands. Also, a procedure is…

正态化变换的大样本行为AI 解读

We investigate the large-sample behavior of the Box-Cox procedures for selecting a transformation to normality. The study of the large-sample behavior clearly reveals the role played by the assumptions. Based on our large-sample results, we introduce an information number approach for transforming a known distribution to near normality. This latter procedure provides bench marks for the maximum amount of improvement achievable through power transformations. We illustrate our…

线性模型中的修剪最小二乘估计AI 解读

We consider two methods of defining a regression analog to a trimmed mean. The first was suggested by Koenker and Bassett and uses their concept of regression quantiles. Its asymptotic behavior is completely analogous to that of a trimmed mean. The second method uses residuals from a preliminary estimator. Its asymptotic behavior depends heavily on the preliminary estimate; it behaves, in general, quite differently than the estimator proposed by Koenker and Bassett, and it…

两组多重时间序列之间共同群时延的估计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…

自相关误差线性回归中普通最小二乘的有限样本效率AI 解读

In the standard linear regression model y = X β + u, with errors following a first-order stationary autoregressive process, it is shown that the relative efficiency of the ordinary least squares (OLS) as compared with the Gauss-Markov estimator depends to a great extent on the X matrix observed. In particular, it is seen that the relative efficiency of OLS increases with increasing correlation for certain cases important in practice. Since this seems to run contrary to what…

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…

单参数指数族的贝叶斯序贯估计AI 解读

The Bayesian sequential estimation problem for one-parameter exponential families is considered using loss related to the Fisher information and linear sampling cost. Tractible expressions for the Bayes estimator and the posterior expected loss are found, and the myopic, or one-step-ahead, stopping rule is defined. Sufficient conditions are given for optimality of the myopic procedure, and the myopic procedure is shown to be asymptotically optimal in all cases considered.

多元位置参数的一类稳健检验与估计AI 解读

Hotelling's T 2 test and the sample mean vector for multivariate location suffer from the same lack of robustness as the univariate t test and sample mean. We propose a class of tests and estimates based on a vector of rank statistics and show that they are easy to compute, have good robustness properties, and are usually more efficient than the classical procedures.

关于 Gamma 分布均值的推断AI 解读

Approximate tests for the mean of a gamma distribution with both parameters unknown are derived. The power of these tests is close to the power of the corresponding uniformly most powerful tests for the mean when the shape parameter is assumed known. The tests are studied by Monte Carlo simulation, and limiting results are also provided as the shape parameter goes to zero or infinity, as well as for the large-sample case. A limited study indicating the nonrobustness of the…