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删失情形下若干非参数检验统计量分布的递归生成AI 解读

The exact distributions of several non-parametric test statistics based on (usually) censored samples are obtained recursively under certain non-parametric classes of alternatives.

Limiting Pitman efficiencies of the sum of squared ranks test relative to best tests for scale alternative detection are obtained for some specific continuous asymmetrical distributions which have mass confined to the positive axis. In particular the A.R.E. of this test to best tests for gamma distributions is maximized (.9372) when the gamma distribution shape parameter is between five and six. Also this test is an asymptotic locally most powerful rank test for detecting…

每对夫妇生育次数差异的随机机制AI 解读

Under certain assumptions a probability distribution for the variation in the number of births per couple has been derived. The distribution involves several parameters. A procedure to find the B.A.N. [best asymptotically normal] estimates of the parameters is outlined. One example of the application of the distribution is discussed in some detail.

单向随机效应模型中均值的贝叶斯估计AI 解读

The problem of estimating the means in the one-way random effect model yjk = θj+ejk is considered from a Bayesian viewpoint. Posterior distributions of the θj are obtained under the assumption that the θj are independently drawn from a Normal population N(θ, σ22) and that the ejk are independent random errors having a N(0, σ21) distribution. It is shown that the posterior distributions of the θj are clustered more closely together than are the corresponding distributions for…

存在缺失观测时多元正态分布的参数估计AI 解读

In this paper a method is developed for estimating the parameters in the multivariate normal distribution in which the missing observavations are not restricted to follow certain patterns as in most previous papers. The large sample properties of the estimators are discussed. Equivalence with maximum likelihood estimators has been established for a subclass of problems. The results of some simulation studies are provided to support the theoretical development.

平稳时间序列创新方差的估计AI 解读

The log of the periodogram is used to estimate the innovation variance of a stationary time series. The difference between the log of the estimated variance of the process and the log of the estimated innovation variance is used as a test for white noise. It is shown that this test is equivalent to Bartlett's test for homogeneity of variances applied to the periodogram without grouping and the asymptotic properties are derived.

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Lehmann 两样本检验的小样本性质考察AI 解读

In this paper we examine how well the asymptotic null distribution of a two sample test due to Lehmann approximates the small sample distribution of the test, compare the validity of this Lehman test with the validity of the two sample t test under the null hypothesis of equal means, and compare the power of this Lehmannn test with the power of the t test. Our general conclusion is that experimenters will prefer to use the t test when the underlying distribution is the scale…

用于回归扰动分析的 BLUS 程序简化AI 解读

This article deals with BLUS residuals in regression analysis, which have the property of being uncorrelated and having constant variance under the null hypothesis that the “true” disturbances have the same property. It is a continuation of the author's earlier article in this journal [7] and the results reported here are the following: (1) the BLUS residuals can be expressed conveniently in terms of the least-squares residuals by means of matrix operations of the order K (K…

异方差数据中的分组估计量AI 解读

This paper gives numerical comparisons of the efficiency of Ordinary Least Squares (OLS) and Grouping Estimators in simple linear regression. The disturbances are assumed to have unequal variances, and an assumption is made about the form of this heteroscedasticity. It is shown that for some types of heteroscedasticity a Grouping Estimator can be more efficient than Ordinary Least Squares.

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利用删失样本估计对数正态分布参数AI 解读

Let g(x) be the ratio of the ordinate and the probability integral of a standardized normal distribution. The local approximation g(x) ≃α + βx is used to derive estimators μc, σc and τc of the parameters of a log-normal distribution, from a type II censored sample. The asymptotic variances and covariances of these estimators are obtained. The estimators are shown to be asymptotically as efficient as the maximum likelihood estimators. Numerical example is presented to give an…

有限总体不等概率抽样中估计量误差方差的上界AI 解读

This paper presents three upper bounds for the variance of an estimator, based on observations selected with varying probabilities from a finite population, the elements of which are ranked with respect to the Y values. Accordingly, the usefulness of these bounds relates to the pre-enumeration analysis where one may well know the intended probabilities and joint probabilities corresponding to the sampling scheme but does not know the Y values. If, however, one can make a…

抽样框含未知重复时的无回答抽样理论AI 解读

Hansen and Hurwitz [3] have developed some non-response sampling theory, using the double sampling method. In this paper, this theory is extended to the case where there is an unknown amount of duplication in the available frame. The theory is developed from the context of a sample survey of beef cattle producers. The available frame was a list of names and addresses of beef cattle producers, whereas the unit of interest was a beef cattle producing operation which could be…

分层子样本数据的方差分析AI 解读

For data selected from a finite population by stratified random sampling with equal probabilities and then randomly and independently assigned within each stratum to subsamples of a fixed number, methods are proposed for the analysis of variance and for testing differences between stratum means, differences between subsample means, and the difference between the sample mean and the mean of the population. The analysis is based on a model for which it is specified that…

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非平衡单因素随机分类中随机效应与观测数量的统计依赖AI 解读

This paper deals with certain aspects of variance component estimation for the unbalanced one-way random classification where the number (Ni ) of observations in the ith class is treated as a random variable not necessarily independent of the class effect (Ai ). It is assumed that in general P(Ni = 0) > 0. The conditional expectations (given the number of observations in each class) of all estimators of the between variance component (σ2 a ) belonging to a certain class of…

近似设定与 k 类估计量的选择AI 解读

This paper carries on work in [2] and [4] on the asymptotic effects of small specification error in simultaneous equation estimation. The specification errors considered are inherent in the approximate nature of econometric models. It is shown that for any parameter and small enough specification error, the probability limits of two-stage least squares and limited-information maximum-likelihood, while different, lie on the same side of the true parameter value, the…

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最优稳健性：一般方法及其在线性位置估计中的应用AI 解读

A general method of determining efficiency-robust estimation and testing methods is presented. This is used to derive admissible linear unbiased estimators (ALUEs) having the following optimality property: Over a specified (finite) family of possible symmetric shapes of the error distribution, the estimator's respective variances cannot be jointly improved. Such estimators are generalizations of Lloyd's best linear unbiased estimators (BLUEs) determined for single shapes.…

多元线性回归中最小二乘的一个定理AI 解读

This note shows that the least squares estimate of the matrix of coefficients in multivariate linear regression model maximizes all the sample canonical correlations between the dependent variables and the linear transformations of the explanatory variables, and it maximizes all the characteristic roots of the sample regression sum of squares and products matrix due to regression of the dependent variables on the linear transformations of the explanatory variables.

关于具有指定边际分布的多元分布的一则注记AI 解读

A method for generating multivariate distributions with marginals in a prescribed family is introduced. It is a straightforward generalization of a method due to Marshall and Olkin.