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二元、两样本及方差分析问题中秩统计量的非零假设模型AI 解读

A nonnull model for rank statistics based on Kendall's tau has received quite a bit of attention in the ranking literature lately. In this article, we analyze this model with an eye towards applying it to situations in which nonparametric statistics such as Kendall's tau, the Mann-Whitney/Wilcoxon U, the Jonckheere-Terpstra statistic, the Kruskal-Wallis statistic, and Friedman's statistic for randomized blocks designs are often used. The data for the basic model are a pair…

Wald 置信区间与检验的若干替代方法AI 解读

The problem considered is that of inference for the variance ratio λ = σ 2 s /σ 2 e in mixed linear models of the form y = Xβ + Zs + e, where β is a column vector of unknown parameters and s and e are statistically independent, multivariate-normal random vectors, with E(s) = 0, var(s) = σ 2 s I, E(e) = 0, and var(e) = σ 2 e I. The case where there is a known upper bound on λ is emphasized. The 100(1 α α)% confidence sets, corresponding to the following two-sided tests of the…

指定年龄下新优于旧约束的生存函数估计量弱收敛AI 解读

A survival function S is said to be in the New Better than Used of age t 0 (NBU-t 0) class if S(x + t 0) ≤ S(t 0)S(x) for all x ≥ 0. Reneau and Samaniego proposed an estimator Ŝ n for S when S is known as a member of the NBU-t 0 class. Many properties of Ŝ n were studied by Reneau and Samaniego. The problems of the weak convergence of Wn = √n (Ŝ n − S), however, was not solved. In this article, we show that the weak convergence of Wn does not hold in general and establish…

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医疗照护模式研究中的贝叶斯与频率学派预测推断AI 解读

The Patterns of Care Studies were conducted to determine the quality of care received by cancer patients whose primary treatment modality is radiation therapy. In this article, we propose and evaluate models which, if acceptable, permit Bayesian and frequentist model-based predictive inference for the desired finite population parameters. Using both hierarchical Bayesian and frequentist mixed linear models, we describe methodology for making the desired inferences,…

评估 DNA 序列非均匀性的若干统计问题AI 解读

The fields of molecular genetics and medicine are accumulating DNA and protein sequence data at an accelerating rate. Discovering and interpreting sequence patterns can contribute to understanding molecular mechanisms and evolutionary processes. This article considers two types of statistical problems in these contexts: (1) identifying anomalies in the distribution of a specified biochemical marker along a DNA string; in particular, new statistical methods are set forth by…

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非参数密度估计的近期发展AI 解读

Advances in computation and the fast and cheap computational facilities now available to statisticians have had a significant impact upon statistical research, and especially the development of nonparametric data analysis procedures. In particular, theoretical and applied research on nonparametric density estimation has had a noticeable influence on related topics, such as nonparametric regression, nonparametric discrimination, and nonparametric pattern recognition. This…

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1851—1985年北半球爆炸性火山活动的探索性分析AI 解读

Studies of regional climate following volcanic eruptions suggest that explosive volcanism exerts a short-term cooling effect. To understand the effects of explosive volcanism on historic temperatures, it is necessary to identify changes through time in the frequency of explosive eruptions. This article presents an exploratory analysis of a record of explosive eruptions in the Northern Hemisphere over the period 1851–1985. This record is modeled as a nonstationary Poisson…

两个相关比例之差的置信区间AI 解读

When data arise as matched binary pairs, it is often of interest to test whether or not the probabilities of an odd pair of each type are equal. Construction of a small-sample confidence interval for the difference in these probabilities is more difficult and either approximate or conservative methods need be resorted to. Two methods are suggested in this article, one a natural asymptotic method and the other a more generally applicable conservative method. The coverage…

概率密度点值估计风险的下界AI 解读

This article considers estimation of f(0) of a density function satisfying a Lipshitz condition in a neighborhood of 0. A nonstandard use of the Cramer-Rao inequality yields numerical lower bounds on the minimax squared error risk of any estimator. These bounds are then compared with the minimax risk of the asymptotically optimal kernel-type estimator. The asymptotic bounds obtained (as the sample size n → ∞) are not quite as good as those in Donoho and Liu (in press a, b),…

基于游程统计量的分布无关对称性检验AI 解读

I present a simple test, based on a runs statistic, for symmetry of a continuous distribution about a known median. The statistic has a binomial sampling distribution and desirable invariance properties. Monte Carlo studies demonstrate that, for a wide variety of alternative asymmetric distributions, the test is more powerful than tests proposed by Butler (1969), Rothman and Woodroofe (1972), or Hill and Rao (1977).

序贯设计实验后的估计AI 解读

We investigate the design of experiments for the nonparametric estimation of the root of an unknown regression function. Approaches to this problem include the Robbins-Monro (1951), Venter (1967), and Lai-Robbins (1979, 1981) stochastic approximation procedures and Wu's (1985, 1986) sequential maximum likelihood estimators. Because the regression function is not assumed to belong to a parametric family, only experimentation near to the root is informative and the sequential…

核密度估计的自助法带宽选择AI 解读

A bootstrap-based choice of bandwidth for kernel density estimation is introduced. The method works by estimating the integrated mean squared error (IMSE) for any given bandwidth and then minimizing over all bandwidths. A straightforward application of the bootstrap method to estimate the IMSE fails because it does not capture the bias component. A smoothed bootstrap method based on an initial density estimate is described that solves this problem. It is possible to…

置信区间覆盖率校正中的自助法迭代AI 解读

Iterated bootstrap procedures may be used to reduce error in many statistical problems. We discuss their use in constructing confidence intervals with accurate coverage and show that bootstrap coverage correction produces improvements in coverage accuracy of order n −1/2 in one-sided intervals, but of order n −1 in two-sided intervals. Explicit formulas are provided for the dominant term in coverage error after iteration in each case. These results are used to compare…

多元测量误差问题中获取真值的二阶段抽样AI 解读

Increasing attention is being given to measurement error models in which the dimension of the proxy or surrogate values is different from that of the missing true values. Even if they are of the same dimension, the error model may not be the simple additive one of observed = true + error, where the error has mean 0. The use of broader models relating true and observed values requires the use of external or internal data containing some true values to calibrate/validate the…

无限方差近单位根时间序列的统计推断AI 解读

An autoregressive time series is said to be near-integrated (nearly nonstationary) if some of its characteristic roots are close to the unit circle. Statistical inference for the least squares estimators of near-integrated AR(1) models has been under rigorous study recently both in the statistics and econometric literatures. Although classical asymptotics are no longer available, through the study of weak convergence of stochastic processes, one can establish the asymptotic…

多元回归的 M 估计AI 解读

Robust alternatives to the seemingly unrelated regression (SUR) estimator of Zellner (1962) are proposed for the classical multivariate regression model. These weighted M estimators achieve an asymptotic covariance matrix analogous to that of the SUR estimator. Comparisons for the l 1, least absolute deviation, case are made with the efficient estimator in the case of elliptically contoured distributions. An example reanalyzing the Grunfeld investment data using a smooth “l…

非参数回归中均值函数差异的 Bootstrap 检验AI 解读

A bootstrap test is proposed for detecting a difference between two mean functions in the setting of nonparametric regression. Error distributions in the regression model are permitted to be arbitrary and unequal. The test enjoys power properties akin to those in a parametric setting, in the sense that it can distinguish between regression functions distant only n −1/2 apart, where n is the sample size. It has exceptional level accuracy, with level error of only n −2, and…

伴随投影寻踪回归AI 解读

Consider a projection pursuit regression model y = g(α + β x) + ε, with an arbitrary monotonic link function g. We assume the link function is unknown; thus we can only estimate the direction of β, that is, the ratios among the components of β, say, β 1/β 2. The direction of β is a useful estimand that measures, say, how many units of x 2 is equivalent to one unit of x 1 in terms of potency in affecting the outcome y. Projection pursuit regression usually solves the equation…

消费者支出调查的样本加权与总量估计AI 解读

The widely used Principal Person method of weighting households in federal government surveys uses external post-Censal information on population to improve survey sample weights by a form of poststratification. While the Principal Person Methodology can be viewed as part of a procedure to adjust for nonresponse and undercoverage, it is not oriented for efficiently incorporating ancillary information or combining information from multiple surveys into survey estimates of…