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二元样本最大值的渐近分布AI 解读

This article investigates the joint distribution, as n→ ∞, of the maxima in a sample of n independent observations of a bivariate random variable (X,Y). A method is presented for deriving the asymptotic distribution of the maxima provided that (1) X and Y possess asymptotic extreme-value distributions and (2) the probability element dF(x,y) has a canonical series expansion. Applied to the bivariate normal distribution, this method confirms the known fact that correlated…

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析因实验中交互作用的非参数检验AI 解读

A measure of interaction in factorial experiments is introduced and the problem of estimating it and testing it for nullity is considered. The asymptotic power efficiencies are studied and Monte Carlo power comparisons are made when samples are drawn from normal and scale contaminated compound normal distributions. The proposed test showed improved power over the normal theory F test and other rank tests for moderately large samples taken from the heavy tailed distributions.

利用部分平衡设计进行半样本重复法方差估计AI 解读

This article considers the use of G-order partially balanced designs for half sample replication method of variance estimation. A new procedure for the arrangement of strata (AAA) is proposed which is shown for a certain class of statistics and for even G to be more efficient than an earlier arrangement (SAOA) when the sequence {a h = W 2 hσ2 hu) is monotonic increasing with either strict downward or strict upward convexity, where W h, is the stratum weight and σ2 hu the…

利用近邻规则重构含噪马尔可夫链AI 解读

An observer desires to record a realization of a stationary two-state Markov chain X, but experimental conditions are such that he instead sees a realization of an error sequence Y. The objective is to reconstruct X. For a simple parameterization of both the Markov chain and the error sequence, a class of near-neighbor reconstruction rules is proposed and investigated. When the values of the parameters are unspecified, estimates are suggested and their asymptotic properties…

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区域人均收入与收入不平等：点估计及其标准误AI 解读

A simple statistical model is developed to assess the implications of random measurement errors in reported per capita incomes and of the bias caused by the use of official exchange rates for (1) regional per capita incomes and (2) regional income inequality. It appears that regional per capita incomes can be estimated with a fair degree of accuracy, provided that the measurement errors of the reported per capita incomes of individual countries are not too highly positively…

统计推断中的稳定分布（一）：对称稳定分布与其他对称长尾分布的比较AI 解读

The hypothesis that very long-tailed data come from a symmetric stable distribution can be generalized, namely, that the observations are generated by a mixture of a normal distribution and another symmetric stable distribution. The difficulty of statistical distinction of the two cases is computed as a function of the various parameters involved. Also, computations show that convolutions of these mixtures can be very slow to converge to the limiting stable distribution or…

分组数据的拟合优度检验AI 解读

Following Riedwyl [8] we generalize some one-sample statistics of the Cramér-von Mises type so that they can be used to test grouped data for goodness of fit. We prove that under the null hypothesis the asymptotic distributions of these statistics, when suitably standardized, coincide with the corresponding classical statistics if the ratio of the sample size to the number of groups (k) remains constant. For k fixed the asymptotic distributions are given under the null…

正态多元线性回归模型中的同时统计推断AI 解读

An F-test of linear hypotheses is compared with Bonferroni t-tests. The individual confidence intervals from Bonferroni t-tests are uniformly shorter than S-intervals implied by the F-test. Power curves are constructed for a few specific alternative hypotheses as functions of the correlation between regressors for the special case of two hypotheses and two regressors. The power of the two procedures is similar when the correlation is small. For highly correlated regressors,…

随机变量之和中项数的估计AI 解读

Fixed sample size and sequential procedures are investigated for estimating the parameter n from observations on a sequence of iid random variables each of which is the sum of n iid random variables with known mean and variance.

k 类估计量：有限样本中的最优归一化AI 解读

Frequently, in estimating an equation, one is interested in a particular set of normalized coefficients. There is still a normalization problem, however, for if an equation contains m 1 endogenous variables, there are m 1 ways to estimate the same coefficients. The purpose of this article is to determine the optimum normalization for finite samples. Restricting the analysis to k-class estimators and employing Kadane's small sample technique [9], let p 2 i denote the…

一种构造预测区间的方法AI 解读

A method is given for obtaining a prediction interval for a variable Y with distribution F Y (y/θ) based on observations x 1, ···, x n from distribution F x (x/θ), where θ is a common parameter to both distributions. The method uses the conditional distribution of y given t, where t is a sufficient statistic for θ in the joint distribution of (X 1, ···, X n , Y). Sample applications are given for the negative exponential and Poisson distributions.

若干非标准情形下最大似然估计量的渐近性质（二）AI 解读

In an earlier article, asymptotic properties of maximum likelihood estimators were found in a class of nonstandard cases when three assumptions were satisfied. The third assumption was rather complicated. In this article it is shown that if we strengthen the second assumption slightly, we can dispense with the third assumption entirely.

一个变量无法直接观测时的相关系数估计AI 解读

The problem is to estimate p the true correlation between two variables x and y when y and u=f(x) (but not x) are measured where f is a monotone function. The monotone correlation coefficient between y and u is defined and shown to be a (strongly) consistent estimator of p. For large samples approximate lower and upper bounds on the sample correlation between x and y are presented. Finally, an application of these results is displayed.

平方根估计量AI 解读

For certain skewed populations there are biased estimators of the population mean, , which have smaller mean square error than the sample mean . This article investigates the properties of the square-root estimator , where . It is shown that this estimator can provide substantial gains in efficiency over when sampling from highly skewed populations. Graphs and tables are presented showing optimum values of C for various types of distributions and sample sizes, and…

分层抽样中的方差估计AI 解读

A procedure is given for estimating variance in stratified sampling whereby two primary selections per stratum are drawn. It estimates the variance of a statistic on the basis of the variabilities among a set of pseudo values computed from partial samples. It is used to estimate the variance of a combined ratio estimator. Both theoretical and empirical findings are encouraging and support the soundness of the proposed scheme for variance estimation.

计量应用中方差分量模型的不同估计量比较AI 解读

The article investigates by means of Monte Carlo experiments the performance of the ML method, the MINQUE method and several other two-step Generalized Least Squares methods in estimating the slope coefficient in a variance components model. It concludes that in models with no lagged dependent variables there is nothing much to choose among these estimators.

尺度参数未知时的位置参数大样本保守检验AI 解读

Potthoff [6] has suggested a conservative test for location based on the Mann-Whitney statistic when the underlying distributions differ in shape. We propose a conservative test based on Mathisen's median statistic [5] and compare its properties to those of Potthoff's test.

利用边际似然函数估计异方差AI 解读

Disturbances in the classical linear regression model that do not have constant variances are said to be heteroscedastic. A vector of standardized residuals is defined whose distribution depends only on the parameters that describe the heteroscedasticity in the model. For the normal case this distribution is used to define a marginal likelihood function on which inferences for these parameters can be based. Then conditionally on an estimate of the heteroscedastic parameters,…

关于非线性中位数估计量的说明AI 解读

Two types of very simple nonlinear median estimators are proposed for even-numbered samples. They are slight modifications of the ordinary sample median. In a Monte Carlo investigation, their efficiency is compared to that of the traditional median. The results indicate that a higher efficiency is achieved by the two types of estimates studied as applied to, respectively, the Cauchy distribution and the family of the normal, triangular and rectangular distributions.

两个正态总体共同均值的固定宽度区间序贯设计：一个方差已知AI 解读

The objective is to provide a fixed-width interval estimator of the unknown common mean of two normal distributions having a prescribed coverage probability and minimal possible sample size. The variance of one distribution is known. The design problem is to decide sequentially while sampling the distribution with the unknown variance when to switch and sample from the distribution with the known variance. New types of boundaries are derived for this sequential design…

抽样理论中若干有用的乘积矩AI 解读

General methods are developed for finding the mathematical expectation of and where X pj denotes the pth (p=1,2,···,k) character of the jth (j=1,2,···, N) unit of a finite population, is the sample mean of the pth character based on a random sample of size n, and is the corresponding population mean. Methods for unbiasedly estimating the product moments are also presented.