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含不等式约束的多元回归：预检验偏差、假设检验与效率AI 解读

This article analyzes, within the context of the standard multiple regression model, the problem of handling inequality constraints specifying the signs of certain regression coefficients. It is common econometric practice when regression coefficients are encountered with incorrect sign to delete the variables in question and reestimate the equation. This article shows that this procedure causes bias and can lead to inefficient parameter estimates. Furthermore, we show that…

检验两个相关矩阵相等的渐近卡方检验AI 解读

An asymptotic χ2 test for the equality of two correlation matrices is derived. The key result is a simple representation for the inverse of the asymptotic covariance matrix of a sample correlation matrix. The test statistic has the form of a standard normal theory statistic for testing the equality of two covariance matrices with a correction term added. The applicability of asymptotic theory is demonstrated by two simulation studies and the statistic is used to test the…

负二项分布及其他聚集型分布的拟合检验AI 解读

A test of fit for the negative binomial and other contagious distributions is presented here. The test, is free of certain disadvantages of the Pearson chi-square test ordinarily used. The proposed test statistic, here called XF 2, is constructed from estimators given by Hinz and Gurland [5] which are obtainable through weighted least squares and which were shown to be highly efficient in wide regions of the parameter space. The power of the proposed test procedure is given…

最大与最小次序统计量近似独立所需的样本量AI 解读

Let Xn and X 1 be the largest and smallest order statistics, respectively, of a random sample of size n. Quite generally, Xn and X 1 are approximately independent for n sufficiently large. Minimum n for attaining at least specified levels of independence are developed. Level of independence is measured by the maximum difference between the true values of P(X 1 ≤x 1, Xn ≤xn ) and the corresponding values assuming independence of Xn and X 1. The results apply to all possible…

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主效应与二因子交互作用正交的最优部分因子设计AI 解读

This article develops some theory of balanced 2m fractional factorial designs which permit estimation of main effects orthogonally to two-factor interactions and the general mean, whose size N is desirably small and which are optimal with respect to the three standard criteria namely, the trace, determinant and the largest root of the variance-covariance matrix of the estimates. The equivalence of these criteria is established for certain situations. For various practical…

摘要暂缺

混合样本的分析方法AI 解读

This article describes the application of the method of moments and the maximum likelihood method to identify the population of origin of each observation when it is thought that the data are a mixture of random observations from two different populations. Specifically, four cases in which both the populations belong to the binomial, the negative binomial, the Poisson or the hypergeometric family are discussed. Both methods also yield estimates of the parameters of the…

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有限总体抽样的最优设计：批判性综述与新研究方向AI 解读

The design of sampling from finite populations is receiving increased attention in the statistical literature. This article presents a critical review of past studies and new developments and outlines areas meriting further study and research. Bayesian and non-Bayesian approaches are analyzed but are not offered in a normative manner. Both points of view and the extent to which they provide differences in survey sample design are discussed and examined. These differences are…

若干常用最小二乘计算程序的数值精度报告AI 解读

Linear least squares test problems based on fifth degree polynomials have been run on more than twenty different computer programs in order to assess their numerical accuracy. The programs tested, all in present-day use, included representatives from several statistical packages as well as some from the SHARE library. Essentially five different algorithms were used in the various programs to obtain the coefficients of the least squares fits. The tests were run on several…

住房质量价值的测量AI 解读

Based on an extensive sample of individual dwelling units, this article estimates the market value, or the implicit prices, of specific aspects of the bundles of residential services consumed by urban households. Quantitative estimates were obtained by regressing market price of owner- and renter-occupied dwelling units on measures of the qualitative and quantitative dimensions of the housing bundle. The measures of residential quality associated with individual dwelling…

若干非参数独立性检验的临界值与经验功效比较AI 解读

A class of nonparametric tests based on the third quadrant layer ranks has recently been studied by Woodworth [12] in connection with the problem of testing for independence in a bivariate distribution. In this article exact one-sided rejection regions are tabulated for the normal score layer rank test which is asymptotically locally most powerful for positive dependence in the bivariate normal distribution. The cut-off points are tabulated for sample sizes n = 4(1)9 and…

若干稳健线性位置估计量的小样本表现AI 解读

Originally, Tukey justified the use of the trimmed mean as a robust estimator because of its high efficiency in large samples from contaminated normal data. The means, variances and covariances of the order statistics in small samples (of size ≤ 20) from a standard normal distribution contaminated by various fractions (.01, .05 and .10) of a normal distribution with mean 0 and scale parameter 3 are derived. The small sample behavior of various robust linear estimators is…

卡方拟合优度检验的最小期望频数与零假设分布近似精度AI 解读

The accuracy of approximations for the null distribution of the chi-square goodness of fit statistic, X 2, is examined numerically for many different multinomial distributions. Some of these approximations are terms of a new asymptotic expansion which provides much greater accuracy than the usual χ2 approximation. When there are too many small expectations, even these are inaccurate, and a diflerent type of approximation must be used—the C(m) distribution. It is proven that…

选择均值最大总体问题中的最优样本量AI 解读

Given k + 1 normal populations, identically distributed with a common known variance σ2 and unknown means, it is required to select N individuals in two stages as follows. In the first stage, n individuals are selected from each of the populations. In the second stage, the remaining N —n(k+1) individuals are selected from the population producing the largest mean in the first stage. A cost unique to the first stage is C(n) = c 0+c 1 na , where C 0, c 1 and α are positive…

变量含误差模型中的最小二乘与分组法估计量AI 解读

The probability density function of the least squares estimator of the slope coefficient in the errors in variables model is presented. It is shown how the bias and mean-square error of the least squares estimator b depend on the parameters of the model. In particular, for a given sample size, b converges to the true parameter as one of the distribution parameters increases indefinitely. The analysis is supplemented with numerical computations of the relative bias and…

利用分组观测估计帕累托定律AI 解读

The problem of estimating the scale parameter in the Pareto distribution from grouped observations is considered. Several estimators—the maximum likelihood estimator and four variants of least squares—are evaluated. Most of these have identical BAN properties but require nonlinear computations. A linearized BAN estimator is constructed, and numerical illustrations are provided.

摘要暂缺

二项概率一致最强检验的序贯修改AI 解读

The early decision version of the uniformly most powerful (UMP) fixed-sample-size test for binomial probabilities, as described for instance by Alling [1], is modified by changing all continuation points which lie on or below a line with specified slope into acceptance points. The modification reduces the average sample number (ASN) for small values of the binomial probability with only a slight loss of power. Approximate formulas for the ASN and power function of the…

马尔可夫链阶数的若干卡方检验：经验评价AI 解读

This article reports a Monte Carlo evaluation of the levels of significance of chi-square tests for the order of two- and three-state Markov chains. Results are consistent with asymptotic theory only when samples are quite large.

利用家庭预算数据时间序列估计动态需求关系AI 解读

The demand parameters are estimated by fitting dynamic and static equations to a time series of Japanese multi-cross-section data using various methods. The results indicate that habit formation is predominant and income is much more important than prices and that it is worthwhile to use dynamic forms.

重新评价厂房与设备投资预期的预测能力AI 解读

This article suggests that anticipations alone do a better job of forecasting business plant and equipment expenditures than fitted functions which include only non-anticipatory data. Anticipations can also make a significant contribution in the presence of such data. Since previously published studies have come to different conclusions, the focus of this article is an evaluation of the methodology and results of those studies.