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回归误差项的贝叶斯分析AI 解读

Properties of realized regression error terms are studied wherein they are treated as unknown parameters. Posterior distributions for individual realized error terms and for linear and certain quadratic functions of them are derived. Posterior moments of measures of skewness, kurtosis, autocovariance, and autocorrelation, defined in terms of the realized errors, are presented, and selected uses of these results indicated in characterizing properties of realized error terms…

随机系数线性回归的有限样本与收敛性质AI 解读

This article studies sampling properties of several unconstrained estimators in the random coefficients model. It is found that the ranking of alternative estimators is sometimes sensitive to selection of true values of the model's parameters. Further, the frequency of negative estimates increases with the size of true variance. Though all estimators converge in 80 to 95 percent of cases, there is generally no efficiency gain at any stage of iterations, possibly because…

空间相互作用模型的估计方法AI 解读

Autoregressive models for spatial interaction have been proposed by several authors (Whittle [15] and Mead [11], for example). In the past, computational difficulties with the ML approach have led to the use of alternative estimators. In this article, a simplified computational scheme is given and extended to mixed regressive-autoregressive models. The ML estimator is compared with several alternatives.

最小二乘解的迭代精化AI 解读

An iterative algorithm for solving linear least squares problems has been developed and tested on an IBM 1620 computer. This article traces the development of the algorithm from that described by Björck and Golub [1] to the present, and shows how, with a slight change in algebra, the Householder triangularization may be replaced equally successfully by the simpler method of Cholesky factorization. The algorithm appears accurate and efficient even for highly ill-conditioned…

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递增失效率分布下次序统计量函数的若干不等式AI 解读

We consider functions which are the sum of the k largest order statistics in a sample of size n from a continuous distribution F, minus nh, where h is a specified constant. We prove that such functions are concave in n. If F is an exponential distribution, then for a fixed k we obtain that value of n which maximizes the expected value of the function defined above. For F IFR we obtain an upper bound on n and also an upper bound on the maximum of the expected value of the…

选择最小方差正态总体的两阶段极小极大程序AI 解读

Given k normal populations with unknown variances and known or unknown means, suppose we wish to select N individuals in two stages as follows: in the first stage, n individuals are selected from each of the k populations; in the second stage, the remaining (N—kn) individuals are selected from the population which gave rise to the smallest variance in the first stage. This article considers a minimax method for determining how large n should be.

序列相关精确检验的一则说明AI 解读

A transformation of the OLS residual vector to achieve a desired covariance structure, proposed earlier by Durbin [3], is shown to be capable of substantially changing the OLS residual vector even when that vector already has nearly the desired covariance structure. This may explain its substantially inferior performance in Monte Carlo comparisons with the transform proposed by the Abrahamse and Koerts [1]. A new transform, involving only small alterations in Durbin's…

相关系数的无偏估计量与序贯检验AI 解读

An unbiased estimator and a Sequential Probability Ratio Test (SPRT) for the correlation coefficient are proposed. The SPRT reduces to the SPRT for a binomial parameter. A comparison is made of the proposed test with those of Kowalski [4] and Choi [1].

分布的最优分组与次序统计量的最优间隔AI 解读

The optimal choice of intervals for grouped distributions is considered from the point of view of maximizing the information on a parameter or maximizing Pearson's φ2. For bivariate distributions, optimal marginal grouping is chosen to maximize (approximately) the correlation. Problems in order statistics from large samples are seen to be related to those for grouped distributions, and the optimal spacing is considered from the point of view of minimizing the asymptotic…

随机系数线性回归：有限样本性质与收敛表现AI 解读

This article studies sampling properties of several unconstrained estimators in the random coefficients model. It is found that the ranking of alternative estimators is sometimes sensitive to selection of true values of the model's parameters. Further, the frequency of negative estimates increases with the size of true variance. Though all estimators converge in 80 to 95 percent of cases, there is generally no efficiency gain at any stage of iterations, possibly because…

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统计分析中的贝叶斯推断AI 解读

Nature of Bayesian Inference Standard Normal Theory Inference Problems Bayesian Assessment of Assumptions: Effect of Non-Normality on Inferences About a Population Mean with Generalizations Bayesian Assessment of Assumptions: Comparison of Variances Random Effect Models Analysis of Cross Classification Designs Inference About Means with Information from More than One Source: One-Way Classification and Block Designs Some Aspects of Multivariate Analysis Estimation of Common…

若干Rényi型检验的功效界AI 解读

Let X 1, X 2, …, Xn be a random sample from a random variable with continuous distribution function H(x). Renyi-type statistics, such as are considered for testing the hypothesis H(x) = F(x) against the class of alternatives G (n)(x), satisfying sup z (F(x) — G (n)(x)) Δ n > 0. Sharp bounds on the power, both for finite sample size and asymptotic values, are obtained for each of the tests examined, and these tests are shown consistent with respect to the class of…

若干非标准情形下似然比的渐近分布AI 解读

In an earlier article [8] conditions were given under which maximum likelihood estimators are asymptotically normal and asymptotically efficient in certain nonstandard cases. Under these same conditions, the asymptotic distribution of the likelihood ratio is found. An easily computed asymptotic equivalent of the likelihood ratio is developed, and is applied to a problem of testing fit.

方差的子集选择问题及其在回归分析中的应用AI 解读

This article presents a subset selection procedure for correlated variances with emphasis on the asymptotic case. An application to selecting the best set of independent variables in a regression problem is given.

齐普夫定律的排名—频数形式AI 解读

Suppose that there are K regions in a country, with Ni people and Mi cities in the ith region. Let Ni be large, Mi random, given Ni , and such that the distribution of M i N i –1, given Ni , converges to a limiting distribution F, with F(x) ∼ Cx γ as x → 0, γ > 0. Let L (r) be the size of the rth largest city in the country. If, given Mi and Ni , there is a Bose-Einstein allocation of the Ni people to the Mi cities in region i, independently for the various regions, then a…

器官移植研究中一种新非参数统计量的渐近正态性AI 解读

This article presents a proof of the asymptotic normality of a recently proposed nonparametric test statistic which has been used in analyzing heart transplant data.