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基于样本分位数的柯西分布参数线性估计AI 解读

Asymptotically best linear unbiased estimates (ABLUE) of the location and scale parameters (when both are unknown) of the Cauchy distribution, based on k order statistics selected from a large sample, are considered. It is shown that the joint asymptotic relative efficiency (JARE) of the two estimates is maximized when the sample quantiles are equally spaced, and expressions are derived for the coefficients used in these estimates. In estimating the scale parameter using a…

二项概率线性组合的 G1 极小极大估计量AI 解读

A G1-minimax estimator for an arbitrary linear combination of binomial probabilities {θi } is derived. Only the mean of each prior distribution is specified. The resulting G1-minimax estimator is shown to be formed by estimating each θi by a weighted average of its prior mean and its maximum likelihood estimate.

位置或尺度参数的修正 Spearman 估计量AI 解读

A method of moments estimator for a location or scale parameter, based on quantal responses, is proposed. The method prescribes Spearman estimation of a generalized moment τ = f G(x) F(dx; θ) where G is a specific distribution in a parametric family of distributions F(·; θ). The choice of design is equal probability spacing with respect to G, i.e., the levels xi are chosen to satisfy G(xi ) = i/(k + 1), where k is the number of levels. General properties of the method are…

关于回归设计中一个典范形式定理的札记AI 解读

A regression design problem leads to applications of a little used canonical resolution of a positive definite matrix. Two algorithms for calculating the resolution are suggested.

随机系数似乎不相关回归的估计AI 解读

This article deals with the problem of estimating the set of seemingly unrelated regressions (SUR) when the regression coefficients are random. In the article, an estimator has been proposed which is consistent and has the same asymptotic normal distribution as the Aitken generalized least squares estimator which assumes the covariance matrix to be known. Further, it has been shown that the proposed estimator is asymptotically more efficient than Zellner's SUR estimator…

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双侧删失数据下生存函数的非参数估计AI 解读

A simple iterative procedure is proposed for obtaining estimates of a response time distribution when some of the data are censored on the left and some on the right. The procedure is based on the product-limit method of Kaplan and Meier [15], and it also uses the idea of self-consistency due to Efron [8]. Under fairly general assumptions, the method is shown to yield unique consistent maximum likelihood estimators. Asymptotic expressions for their variances and covariances…

Theil 相容性检验统计量的精确有限样本分布及应用AI 解读

In this article we derive the exact finite sample distribution of a statistic utilized by Theil [10] to test whether sample and prior information are in conflict with each other. A weighted estimator for the slope coefficient in a simple regression equation with one independent variable is obtained by using weights which are determined by the observed value of Theil's test statistic. This weighted estimator is particularly useful when we are uncertain about the compatibility…

错误模型与数据分析后的模型构建AI 解读

This article proposes a method of discounting evidence when linear regression models are constructed after the data have been partially analyzed. The solution parallels a formal decision theoretic analysis of a presimplification problem in which models or model spaces are simplified before observation in order to avoid observation or processing costs. Post-data model construction is interpreted as the data-dependent decision that this pre-simplification is undesirable. The…

心脏移植数据的生存分析AI 解读

This article presents a number of parametric and nonparametric approaches to the analysis of nonexperimental heart transplant data from the Stanford Heart Transplantation Program, and attempts to come to some conclusion regarding whether heart transplantation is life-extending.

基于随机变量比值的比例多重性估计AI 解读

This article applies the counting rule strategy to the problem of estimating the proportion of population elements with a specified characteristic based on a sample of enumeration units. The distribution of population elements among the enumeration units is a function of the counting rule which specifies the conditions for linking population elements to enumeration units. The counting rule strategy involves the selection of the counting rule which minimizes the variance of…

错误知识模型下选择题评分的经验贝叶斯方法AI 解读

This article develops multiple-choice test scoring rules, concentrating on Bayes rules and their frequency theory analogs, empirical Bayes rules. Conditions are given for empirical Bayes estimates to lie in the probability simplex. The misinformation model is considered in detail. It is shown that ranking by raw scores is equivalent to ranking by Bayes scores when the loss function increases with error and the sampling distribution has the monotone likelihood ratio property.…

法院服务需求的测量：对联邦地区法院案件权重的批评AI 解读

The case weights used by the Federal District Courts are evaluated in conceptual terms and in terms of the sample design used recently to reestimate the weights. The weights are shown to be conceptually inferior to another set and to be seriously underestimated. A closed form expression is derived for the underestimation bias and is used to show the probable magnitude of the underestimation.

季节调整与变量之间的关系AI 解读

This article studies the effect of official seasonal adjustment procedures on the relations between variables. By considering time-invariant linear filters, and in particular a linear approximation to the Census Method II adjustment program, the effect of adjusting one or both of the variables in a distributed lag relation is examined, and the distortions which can arise are described. Applying the actual (nonlinear) adjustment procedure to artificial data indicates that at…

Wilcoxon 符号秩统计量分布的正态与 Edgeworth 近似精度AI 解读

Cumulative probabilities from the null distribution of the Wilcoxon signed rank statistic were approximated by the normal approximation and by Edgeworth expansions to terms of order 1/N and of order 1/N 2 for selected values of the statistic for values of N from 30 through 100. Use of the usual correction for continuity is advantageous at all probability levels in the Edgeworth expansions and in the normal approximation for probability levels greater than about 0.035. The…

Weibull 模型的最大似然估计AI 解读

Some of the questions concerning the uniqueness of the maximum likelihood estimates for the parameters in the Weibull distribution are considered for both censored and noncensored samples. In some cases answers previously known are reviewed, while new results are presented for some other cases. In particular, it is shown that with the shape parameter known, the maximum likelihood estimates of the location and scale parameters exist and are unique. Also, the case in which all…

柯西分布参数估计问题的最优解AI 解读

It is shown that for the estimation of the location parameter of a Cauchy distribution, for which the scale parameter is known, k-spacings corresponding to the maximum asymptotic relative efficiency (ARE) are asymmetric when k = 4m − 1; this result is in contrast to Chan's assumption that optimal k-spacings are always symmetric. Accurate solutions for the maximal ARE and optimal k-spacings obtained by a combination of dynamic programming and Newton-Raphson iterations have…

截断或删失 Poisson 分布的最大似然估计AI 解读

The results derived by Blight [1] for the exponential family of distributions are applied to the Poisson case. A table is given to simplify the estimates of the Poisson parameter for data that are censored or truncated on the left or the right.

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利用初始估计改进线性模型系数估计AI 解读

A procedure which utilizes an initial estimate to estimate the coefficients in a linear mode is introduced. A linear model containing replications with the same input matrix is considered and a class of two-stage estimators is defined. Optimal estimators in the class are determined, and it is shown that the proposed estimators are better than the corresponding single-sample least squares estimator if the initial estimate is accurate, and are as good (asymptotically) as the…

用交叉验证确定回归模型的样本量AI 解读

A cross-validation approach to the a priori determination of sample size requirements and the a posteriori estimates of the validity of a derived regression equation is developed for regression models, where sampling from multivariate normal populations is discussed in particular. Tables of sample size estimates are presented for the random model and their applications illustrated. An algorithm is given to obtain tables for the fixed model directly from those for the random…

变量含测量误差的回归模型中斜率的一致估计AI 解读

Consistent estimators for the slope coefficient in a regression model, where both variables are subject to errors, do not exist without some restrictions on the model. When the serial correlation of (lag 1) of the regression is known to be nonzero, one can obtain extra information from the first differences and get a consistent estimator for the slope. It turns out that this estimator is (asymptotically) equivalent to an estimator which uses as instrumental variable the…

小样本升降法中若干中位反应估计量的均方误差比较AI 解读

Mean square errors associated with median response estimates are compared for the normal and logistic distributions, based on both maximum likelihood and minimum chi square analyses. In broad perspective there is little difference among the mean square errors for these four estimates, regardless of sample size and stimulus level spacing. The first three of the median response estimates require an iterative numerical solution, whereas the minimum chi square analysis for the…