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有限总体样本的非参数贝叶斯模型AI 解读

Summary Using Ferguson's (1973) non-parametric priors in a Bayesian analysis of finite populations, we show that asymptotically, at least, the usual estimates and confidence intervals for the population mean in simple and stratified random samples can be justified in Bayesian terms. We then apply these models for estimating population percentiles, and a new procedure for interval estimates in stratified sampling is developed.

不连续分布下 Smirnov 型两样本秩检验的分布AI 解读

Summary An important area of application for rank tests occurs when there are ties in the data which may happen when the observations are drawn from a discrete population or are grouped. The standard theory for the two-sample Smirnov test as to whether two samples have been drawn from the same population assumes continuous distributions in which case ties only arise with probability zero. The null distribution of the test statistic for large sample sizes is obtained here for…

有限信息极大似然估计量分布函数的计算AI 解读

T. W. Anderson, Naoto Kunitomo, Takamitsu Sawa, Evaluation of the Distribution Function of the Limited Information Maximum Likelihood Estimator, Econometrica, Vol. 50, No. 4 (Jul., 1982), pp. 1009-1027

加权 L² 分位数距离估计量的渐近性质AI 解读

The asymptotic properties of a family of minimum quantile function distance estimators are considered. These procedures take as the parameter estimates that vector which minimizes a weighted $L^2$ distance between the empirical quantile function and an assumed parametric family of quantile functions. Regularity conditions needed for these estimators to be consistent and asymptotically normal are presented. For single parameter families of distributions, the optimal form of…

乘积极限估计量的渐近最优性AI 解读

The product limit estimator due to Kaplan and Meier (1958) is well-known to be the nonparametric maximum likelihood estimator of a distribution function based on censored data. It is shown here that the product limit estimator is an asymptotically optimal estimator in two senses: in the sense of a Hajek-Beran type representation theorem for regular estimators; and in an asymptotic minimax sense similar to the classical result for the uncensored case due to Dvoretzky, Kiefer,…

历史身高的估计AI 解读

Historical samples of military, naval, and merchant marine heights suffer from undercounts of short people, undercounts highly irregular compared to the truncated distributions for which standard methods are available. Our knowledge is too imprecise for parametric models of the undercount process but it suffices for intuitive description of the deviations from normality with which estimators should cope. Two new estimators are developed. The first adapts maximum likelihood…

独立同分布误差线性模型的经验分位数函数AI 解读

The regression quantile statistics of Koenker and Bassett (1978) are employed to construct an estimate of the error quantile function in linear models with iid errors. Some finite sample properties and the asymptotic behavior of the proposed estimator are derived. Comparisons with procedures based on residuals are made. The stackloss data of Brownlee (1965) is reanalyzed to illustrate the technique

摘要暂缺

利用经验特征函数估计柯西分布的位置与尺度AI 解读

The iterative method for the parameter estimation of stable laws proposed by Koutrouvelis (1981) is modified to handle the case where the distribution is assumed to belong to a Cauchy family with location and/or scale parameter unknown. It is shown that the determination of optimum values at which the empirical characteristic function needs to be evaluated reduces in this case to the determination of the asymptotically optimum quantiles for the parameter estimation of an…

指数分布分位数的估计AI 解读

We consider the problem of estimating a quantile ξ + bσ of an exponential distribution on the basis of a random sample of size n ≥ 2. Here ξ and σ are unknown location and scale parameters and b is a given constant. For quadratic loss, it is established that the best equivariant estimator is inadmissible if 0 ≤ b < n-1 or b > 1 + n 1. For b > 1 + n 1 the estimator elsewhere, provides a noticeable improvement over δ0.

广义 F 分布的卷积AI 解读

The generalized F variate is the ratio of two independent gamma variates, and its distribution includes as special cases such distributions as the inverted beta, Lomax, and Snedecor's F, Based on convolution, the distribution function of the sum of two independent generalized F variates is derived in terms of a Lauricella-Saran hyper-geometric function of three variables. The results are applied, with numerical examples given, to (a) a Bayesian analysis of the availability…

摘要暂缺

基于两个对称次序统计量的 t 统计量有限样本分布：正交象限概率表示AI 解读

A t statistic based on two symmetric order statistics is defined. When the underlying distribution of the data is Gaussian the distribution function of the t statistic is shown to equal a linear combination of orthant probabilities with a specific form for the covariance matrix.

对称分布的非参数估计AI 解读

Substantial improvements in the accuracy of nonparametric estimates are achieved when the centre of a symmetric distribution is known. Resultant benefits for confidence bands for the distribution function are extended to confidence intervals for quantiles and also tolerance limits. When the symmetry centre is not known and must be estimated from the sample improvements in accuracy are still possible.

一种新的分布无关分位数估计量AI 解读

A new distribution-free estimator Qp of the pth population quantile is formulated, where Qp is a linear combination of order statistics admitting a jackknife variance estimator having excellent properties. The small sample efficiency of Qp is studied under a variety of light and heavy-tailed symmetric and asymmetric distributions. For the distributions and values of p studied, Qp is generally substantially more efficient than the traditional estimator based on one or two…

广义 Behrens–Fisher 问题的 Mood 中位数检验修正AI 解读

A modification of Mood's median test is described which allows one to test for differences between two medians without making any assumptions on the shapes of the underlying populations. The proposed procedure is exactly distribution-free when the populations have the same shape and is asymptotically distribution-free when they do not. It is the retention of the exact distribution-free property when the populations have the same shape which distinguishes the proposed…

利用经验特征函数估计柯西分布的位置与尺度AI 解读

SUMMARY The iterative method for the parameter estimation of stable laws proposed by Koutrouvelis (1981) is modified to handle the case where the distribution is assumed to belong to a Cauchy family with location and/or scale parameter unknown. It is shown that the determination of optimum values at which the empirical characteristic function needs to be evaluated reduces in this case to the determination of the asymptotically optimum quantiles for the parameter estimation…

相依多样本下 Kruskal–Wallis 检验的渐近保守性与效率AI 解读

The robustness (asymptotic conservativeness) of Kruskal-Wallis test under certain departures from mutual independence of K univariate samples is established. This robustness provides a procedure for testing the equality of K marginal distribution functions based on a broken random sample from a K-variate distribution that satisfies a mild condition. For the unbroken sample, a generalized Kruskal-Wallis (KW) test is proposed for testing the symmetry of a K-dimensional…

相关样本下 Kruskal–Wallis 检验的渐近保守性与效率AI 解读

The robustness (asymptotic conservativeness) of Kruskal-Wallis test under certain departures from mutual independence of K univariate samples is established. This robustness provides a procedure for testing the equality of K marginal distribution functions on a broken random sample from a K-variate distribution which satisfies a mild condition. For the unbroken sample, a generalized Kruskal-Wallis test is proposed for testing the symmetry of a K-dimensional distribution…

Bootstrap 的若干渐近理论AI 解读

Efron's "bootstrap" method of distribution approximation is shown to be asymptotically valid in a large number of situations, including $t$-statistics, the empirical and quantile processes, and von Mises functionals. Some counter-examples are also given, to show that the approximation does not always succeed.

Efron bootstrap 的渐近准确性AI 解读

In the non-lattice case it is shown that the bootstrap approximation of the distribution of the standardized sample mean is asymptotically more accurate than approximation by the limiting normal distribution. The exact convergence rate of the bootstrap approximation of the distributions of sample quantiles is obtained. A few other convergence rates regarding the bootstrap method are also studied.

位置参数与拟合优度的最小距离估计AI 解读

A weighted Cramér-von Mises distance between the empirical distribution function and the assumed model F0(x - θ) is minimized to produce estimators θ n that are asymptotically normal. If the weight function is taken proportional to (- ln f 0)″/f 0 , then θ n is asymptotically efficient and the minimized distance has the appropriate loss of one degree of freedom. Special attention is focused on the limiting distribution of this latter goodness-of-fit statistic in both null…

模型误设下位置与尺度参数的最小均方距离估计AI 解读

The paper is concerned with estimating location and scale parameters by estimators minimizing a mean squared distance between the empirical distribution function and a conveniently chosen parameterized distribution function. Within the true parametric family the location estimator has the same asymptotic distribution as that of Hodges & Lehmann. If the underlying distribution is not a member of the assumed parametric family, the questions concerning bias, rather than…

由 n 维立方体上随机变量确定的分布AI 解读

The distribution function of a random variable of the form $\sum^n_{i = 1} a_i Y_1 Y_2 \cdots Y_i$ where $a_i > 0$ and $0 \leq Y_i \leq 1$ is considered. A geometric argument is used to obtain the distribution function as a repeated integral. The result is used first to obtain the distribution function of a linear combination of variables defined over the simplex $X_i \geq 0, \sum^n_{i = 1} X_i \leq 1$. As a second application the distribution of certain quadratic forms over…