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删除样本中的极端观测对时 Kendall 秩相关估计的偏差AI 解读

This article obtains the average effect on the estimator of Kendall's rank correlation coefficient when extreme pairs are removed from a sample. Formulas, which are functions of Sterling numbers of the second kind, are derived for this bias. The exact bias, and an approximation, are tabulated for n = 3(1) 19.

损失函数未完全指定时的估计：多个位置参数情形AI 解读

If p ≥ 3 separate normal means are to be estimated, the usual, invariant estimator is “inadmissible” if the p separate loss functions can be pooled into a single loss function for the ensemble-of-means problem. Here, we formulate a version of the problem where the losses cannot be pooled in this way, and find a surprisingly weak necessary and sufficient condition under which the usual estimator is inadmissible in a sense appropriate to this formulation. We also examine the…

不完全区组设计中区组间与区组内组合估计的精确方差AI 解读

This article presents methods for evaluating exact variance of combined inter- and intra-block estimates of treatment effects in incomplete block designs. The results are valid for all incomplete block designs and hold for a wide class of combined estimates including most in the literature. Tables of exact variance for some estimates are presented for some balanced designs and for some partially balanced designs.

递增失效率分布中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…

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.

非线性回归模型中位置参数似然比检验的功效AI 解读

The Likelihood Ratio Test statistic, T, is considered for the hypothesis H: θ = θ0 against A: θ ≠ θ0 in the nonlinear regression model y = f(x, θ) + e with normal errors and unknown variance. The distribution function of a random variable X such that n · (T — X) converges in probability to zero is derived. Using X to approximate T, the power of the Likelihood Ratio Test is tabulated for selected sample sizes and departures from the null hypothesis. The adequacy of the…

主成分回归的最小方差性质AI 解读

In the context of the usual regression model, , this article shows that the coefficient obtained when Y is regressed on the first principal component of the independent variables may be interpreted as an estimator of that , which can be estimated with least variance. Analogous results hold for succeeding components, and the property can be expressed in terms of volumes of confidence ellipsoids. To estimate using r principal components, choice of those components associated…

一个变量存在缺失时的均值相等检验：蒙特卡洛研究AI 解读

This article is concerned with the relative merit of the procedures proposed by Lin [2], Metha and Gurland [3], and Morrison [5] for testing the equality of means of a bivariate normal distribution with correlation ρ and common variance σ2 when some observations on one variable are missing. A Monte Carlo study of the powers and level of significance is conducted. Comparisons among these tests and the paired t test are made. The preferred test is established for each…

选择方差最小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.

方差的子集选择问题及其回归分析应用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.

关于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距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…

位置尺度族中次序统计量的最佳线性无偏预测AI 解读

In many life testing, reliability and replacement policy situations, it is desirable to predict the time of future failures from times of the early failures in the same sample. Interval prediction in this setting has been treated by several authors. In this article, the authors give best linear unbiased (blu) point predictors of future failures when the underlying distribution is known up to location and scale. Analogous large sample procedures based on sample quantile…

一种简单的稳健回归方法AI 解读

Estimates of the parameters of a linear model are usually obtained by the method of ordinary least-squares (OLS), which is sensitive to large values of the additive error term. By dividing the sample into nonoverlapping subsamples and computing the trimmed means of OLS subsample regression coefficients, we obtain a simple, consistent and asymptotically normal initial estimate of the coefficients, which protects the analyst from large values of ∈ i which are often hard to…

检验Almon滞后法的约束AI 解读

This article considers testing the restrictions imposed by Almon's approach to estimation of distributed lag relationships. The conventional likelihood ratio test procedure requires that the regression equation be estimated in unrestricted form and then subject to the Almon restrictions. An alternative test is suggested which has the advantage of requiring only that the unrestricted version be estimated. The problem of selecting the order of the polynomial is discussed and a…

计量经济估计量性质的蒙特卡洛比较研究AI 解读

Together with straightforward simulation, this study makes use of antithetic-variate and control-variate techniques in investigating the properties of econometric estimators. It is shown that when the covariances between the disturbances are small, the results on the relative standing of the estimators are indeterminate; but when they are sufficiently large, full-information methods are superior to single-equation methods. FIML gave the best performance and 2SLS was the best…

作为访问偏向记忆的“解释结果”AI 解读

This article presents an inference-cum-memory model with uncertain parameter p and binomial data. The model is intended to represent the phenomenon especially common in the social sciences of explaining the results of a statistical calculation. The principal assumptions of the model are that experiments, not sufficient statistics, are stored in memory, and that the experiments are categorized by and accessed according to their implications for inference. The nonsample…

利用薪资数据估计百分位回归线AI 解读

In case of contamination, skewness or unequal variances, a nonparametric alternative to least squares regression is considered. In addition, investigators are often more interested in estimates of percentile lines than in the mean regression line. Thus, a modification of Brown-Mood regression is proposed to estimate the (100p) th percentile line α + βx of a random variable. This technique is applied to some data (artificial, but similar to real) relating the salary (y) of a…

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…

渐近最佳线性估计量最优分位点选择的统一方法AI 解读

Due to its computational simplicity and efficiency, asymptotically best linear estimates (ABLE) based on order statistics selected from a complete, or censored, sample are of particular importance. This article deals with a unified method for finding the optimum spacing (eventually the optimum rank of the order statistics) for the ABLE. Application of the method estimating one of the two (location and scale) parameters of various distributions is also discussed.