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判别与百分位数置信带AI 解读

Using the general linear model, y = Xβ+e, where e∼N(0, σ2/): simultaneous confidence bonds are found for the 100 pth percentile, x′β+kpσ, of the normal population with mean x′β and variance σ2 (kp is the 100 pth percentile of the standard normal distribution). The bands are simultaneous in x or in x and p. In the simple linear regression case these bands are used to define simultaneous discrimination sets for any fixed values, yP, of the dependent variable.

量身定制的测验：随机逼近的一项应用AI 解读

Some stochastic approximation procedures are considered in connection with the following problem. How shall we choose a sequence of test questions in order to estimate as accurately as possible a given examinee's standing on some psychological dimension? Illustrations are given evaluating certain procedures in a specific context.

次序统计量取值范围的界AI 解读

Let x1x2 ··· xn be any set of number satisfying Σ xi=0 Σ xi 2=1. There are bounds on the range of xi when the set {xi} is ranked (a) by x1≥x2≥ ··· ≥ xn and (b) by |x1|≥|x2|≥ ··· ≥|xn|. These bounds are given. The applicability to finite populotionr is pointed out.

存在缺失数据时均值差的估计方法AI 解读

The maximum likelihood estimate of the difference of the means is obtained in sampling from a bivariate normal distribution with unknown variances and co-variance when some of the observations on one of the variables are missing. This estimate is compared to several others by using the mean square error criterion. It is found that, when there are a moderate number of complete pairs of observations, the maximum likelihood estimate has the smallest mean square error for most…

条件似然比检验的渐近分布AI 解读

A conditional likelihood ratio test for testing a hypothesis concerning structural parameters in the presence of infinitely many incidental parameters is suggested. It is shown that the usual X2 approximation to the log-likelihood ratio fails to work in many situations involving incidental parameters. In contrast it is shown that the X2 approximation can be used in large samples under fairly general assumptions if we use conditional likelihood ratio tests instead. The…

均匀分布参数的序贯估计AI 解读

The main problem to be solved here may be described as follows: Let X1, X2, ··· be independent random variables, each with density fθ(x) = 1/θ over (0, θ) and zero elsewhere. It is desired to estimate the unknown parameter θ by an interval of length at most d units and with confidence at least 1 −α, for some specified d>0 and α in (0, 1). An exact solution and an asymptotic theory for a sequential procedure are given in Sections 1 and 2, respectively. The procedure proposed…

位置参数的效率稳健系统线性估计量AI 解读

Several classes of efficiency-robust linear unbiased estimators of location based on k sample quantiles are defined. The efficiencies of these estimators under the normal, logistic, and double exponential distributions are computed for sample sizes n = 20, 30, 40, 50, 100, ∞, and subsamples of size k = 2, 6, 10, 20. These results are then discussed in relation to other research in efficiency-robust estimation.

正态分布尾概率的最优无偏估计与最大似然估计的均方误差AI 解读

Formulas for the variance of the uniformly minimum variance unbiased (UMVU) estimator, and of the mean square error (MSE) of the maximum likelihood (ML) estimator, of tail probabilities of normal distributions are derived. Relative efficiency values of these estimators of samples of size 6, 12, 18 and tail probabilities .025, .05, .10, .2, .3, .4, .5 are presented. The bias of the ML estimator for these cases is also given. The formulas developed involve incomplete moments…

两个变量均有测量误差时的直线回归估计札记AI 解读

Let yi = α + βxi + εis xi = ξi + δis i = 1, 2, ···, N, N ≥ 3, where (εis δi)s i = 1, 2, ···, N are independent bivariate normal with zero means, variances σ ε2 σδ2 and correlation ρ, the ξi being unknown constants at least two of which are distinct. Let τ = (N−1)−1 ΣN i=1 (ξi − ξ)2/Σ δ2 and let . A recent article by Richardson and Wu gives, among other things, the expected value and m.s. error of b, when ρ = 0. This note generalizes their results, using a different method,…

分类数据的方差分析AI 解读

A measure of variation for categorical data is discussed. We develop an analysis of variance for a one-way table, where the response variable is categorical. The data can be viewed alternatively as falling in a two-dimensional contingency table with one margin fixed. Components of variation are derived, and their properties are investigated under a common multinomial model. Using these components, we propose a measure of the variation in the response variable explained by…

美国农业部农场房地产净投资序列：方法批评AI 解读

This article documents and appraises the methodology and data sources used in deriving the USDA series on net investment in farm real estate. The series has been used in many studies dealing with the farming sector of the U. S. economy, but the USDA procedures are shown to be highly questionable on theoretical grounds. Several likely sources of bias and measurement error are pointed out. Suggestions for improving the series, and some alternative methods of estimation are…

多参数情形下最大似然迭代程序的收敛问题AI 解读

In multiparameter situations there are important problems of convergence in the solution of maximum likelihood iterative equations. Convergence may be critically dependent on the initial parameter estimates employed. These problems are indicated specifically for a model of exponentially-distributed lifetimes where the reciprocal of the exponential parameter is linearly dependent on various regressor variables. A strategy is suggested based on alternative use of observed or…

控制非正态变量均值的最优样本量与抽样间隔AI 解读

Following Duncan [3], the per hour cost of the process under the surveillance of a mean chart for controlling the mean of non-normal variables whose density function is represented by the first four terms of an Edgeworth series is obtained. The sample size and sampling interval which minimize the cost for detecting a particular shift in the process average are derived when the width of the control limits is specified. They are numerically determined for different non-normal…

泊松参数乘积与商的假设检验、置信区间及可靠性应用AI 解读

X1 X2, ···, Xk1, Y1, Y2, ···, Yk2 are k1 + k2 mutually independent Poisson random variables with parameters λ1, λ2, ···, λk1, μ1, μ2, ···, μk2, respectively. Confidence intervals and tests of hypotheses for the parameter θ = λ1λ2 ··· λk1 / μ1μ2 ··· μk2 are obtained. Under suitable conditions these procedures may be used to obtain approximate confidence intervals and tests of hypotheses of the parameter ρ = ρ1ρ2 ··· ρk1/ρk1+1ρk1+2 ··· ρk1+k2, where the ρi's, i = 1, 2, ···, k1…

缺失数据下多元正态参数极大似然估计的期望与方差AI 解读

Exact expectations and variances have been obtained for the maximum likelihood estimates of the elements of the mean vector and covariance matrix of the multivariate normal distribution when a subset of the variates does not have observations on some sampling units. The biases, variances, and mean square errors of the estimates are compared with those of the usual estimates computed from the complete observation vectors. When the correlations between the complete and…

若干不相关与独立的秩统计量AI 解读

Some interesting examples of uncorrelated simple linear rank statistics are listed. Consideration is then given to conditions under which general rank statistics are uncorrelated or have joint distributions which enjoy certain symmetric properties. Two simple linear rank statistics that are uncorrelated are found, under suitable restrictions, to be asymptotically independent. This is followed by some illustrations in which two rank statistics are exactly independent. The…

估计中的偏差减少AI 解读

A general procedure for reducing the bias of point estimators is introduced. The technique includes the “jackknife” as a special case. The existing notion of reapplication is shown to lack a desirable bias removal property for which it was originally designed. Proper reapplication is proposed to conform to the general notion of higher order bias elimination and an interesting algorithm for the correct method is defined. Illustrative examples are drawn from ratio estimation,…

检验最小二乘回归程序舍入误差的新方法AI 解读

A new, easily applied method for examining any least-squares computer program for internal consistency is given. Only one data set is necessary, and by making appropriate transformations on these data results are given to provide an internal check on the accuracy (or consistency) of the given program. Accuracy becomes an increasing problem, of course, when the original data set is ill-conditioned. The theorems and proofs necessary to the method are presented as well as a…

相关测量误差与回归系数的最小二乘估计AI 解读

This article explores, for a set of survey conditions, the effect of correlated measurement error on the ordinary least squares estimator of the regression coefficient for a finite bivariate population, when both variables are subject to correlated measurement error. The sample estimates for some selected housing variables show that the average of the correlated measurement error components have little effect, but the simple response variance and covariance have pronounced…

摘要暂缺

摘要暂缺

两个变量均含误差时直线回归估计的一则说明AI 解读

Let yi = α + βxi + εis xi = ξi + δis i = 1, 2, ···, N, N ≥ 3, where (εis δi)s i = 1, 2, ···, N are independent bivariate normal with zero means, variances σ ε2 σδ2 and correlation ρ, the ξi being unknown constants at least two of which are distinct. Let τ = (N−1)−1 ΣN i=1 (ξi − ξ)2/Σ δ2 and let . A recent article by Richardson and Wu gives, among other things, the expected value and m.s. error of b, when ρ = 0. This note generalizes their results, using a different method,…

无应答问题中的多阶段抽样AI 解读

The sampling procedure involving subsampling of nonrespondents is discussed. A rule for selecting a subsample of nonrespondents is proposed under which the subsampling fraction is not kept constant, but varied according to the sample nonresponse rates. Using this sampling rule, the variance of the estimator of the population mean is independent of the unknown rate of nonresponse in the population. This rule provides a procedure for determining the initial sample size and…