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十人应战：估计足球比赛中红牌的影响AI 解读

We investigate the effect of the expulsion of a player on the outcome of a soccer match by means of a probability model for the score. We propose estimators of the expulsion effect that are independent of the relative strength of the teams. We use the estimates to illustrate the expulsion effect on the outcome of a match.

列联表中的拟独立与拟依赖：兼论有序三角列联表AI 解读

In the usual statistical analysis of the entries (frequencies) in a contingency table having I rows and J columns (I ≥ 2, J ≥ 2), an important role is often played by the usual null hypothesis of independence (i.e., the hypothesis that the row variable and the column variable are statistically independent of each other). In the situation considered in this article, the entries in some of the I × J cells of the contingency table are omitted from the analysis (because these…

游程的分布理论：马尔可夫链方法AI 解读

The statistics of the number of success runs in a sequence of Bernoulli trials have been used in many statistical areas. For almost a century, even in the simplest case of independent and identically distributed Bernoulli trials, the exact distributions of many run statistics still remain unknown. Departing from the traditional combinatorial approach, in this article we present a simple unified approach for the distribution theory of runs based on a finite Markov chain…

利用估计函数分析复杂调查数据AI 解读

We describe a method for point and interval estimation of population parameters from complex surveys using estimating functions. The theory was originally developed for infinite populations and has recently been applied to finite populations. With estimating functions, a unifying framework can be given for point and interval estimation of both finite and infinite population parameters. We discuss test inversion methods to derive confidence intervals for one-dimensional…

用二元数据测量潜在子群变化：无条件、条件与半参数极大似然估计AI 解读

Changes in dichotomous data caused by treatments can be analyzed by means of the so-called linear logistic model with relaxed assumptions (LLRA). In contrast to models of the Rasch type, the LLRA allows incidental multidimensional parameters describing the response behavior of the subjects so that each observable criterion used for assessing the changes is governed by its own subject parameter. Because generalizability of the treatment effects over subjects and criteria is…

右删失两样本问题中位移函数的推断及应用AI 解读

For two distribution functions, F and G, the shift function is defined by Δ(t) = G −1 · F(t) - t. The shift function is the distance from the 45° line and the quantity plotted in Q-Q plots. In the analysis of lifetime data, A represents the difference between two treatments. The shift function can also be used to find crossing points of two distribution functions. The large-sample distribution theory for estimates of Δ is studied for right-censored data. It turns out that…

在干扰参数置信集合上最大化的 p 值AI 解读

For testing problems of the form H 0: v = v 0 with unknown nuisance parameter θ, various methods are used to deal with θ. The simplest approach is exemplified by the t test where the unknown variance is replaced by the sample variance and the t distribution accounts for estimation of the variance. In other problems, such as the 2 × 2 contingency table, one conditions on a sufficient statistic for 0 and proceeds as in Fisher's exact test. Because neither of these standard…

单侧多变量问题中一致更有功效的检验AI 解读

We consider a testing problem in which a normal mean vector is at the origin under the null hypothesis and in a cone under the alternative and the covariance matrix is unknown. Perlman studied the likelihood ratio (LR) test and found that it is biased and hence does not compare favorably with Hotelling's T2. We point out that certain tests of Perlman are uniformly more powerful as well as simpler than the LR test. These are the corresponding LR tests when the alternative is…

走向贝叶斯与频率学派点估计的协调AI 解读

The Bayesian and frequentist approaches to point estimation are reviewed. The status of the debate regarding the use of one approach over the other is discussed, and its inconclusive character is noted. A criterion for comparing Bayesian and frequentist estimators within a given experimental framework is proposed. The competition between a Bayesian and a frequentist is viewed as a contest with the following components: a random observable, a true prior distribution unknown…

利用平方累积和回顾检测方差变化AI 解读

This article studies the problem of multiple change points in the variance of a sequence of independent observations. We propose a procedure to detect variance changes based on an iterated cumulative sums of squares (ICSS) algorithm. We study the properties of the centered cumulative sum of squares function and give an intuitive basis for the ICSS algorithm. For series of moderate size (i.e., 200 observations and beyond), the ICSS algorithm offers results comparable to those…

利用复合估计量实现高维多元位置与形状的可计算稳健估计AI 解读

Estimation of multivariate shape and location in a fashion that is robust with respect to outliers and is affine equivariant represents a significant challenge. The use of compound estimators that use a combinatorial estimator such as Rousseeuw's minimum volume ellipsoid (MVE) or minimum covariance determinant (MCD) to find good starting points for high-efficiency robust estimators such as S estimators has been proposed. In this article we indicate why this scheme will fail…

部分回归变量并非始终可观测时的回归系数估计AI 解读

In applied problems it is common to specify a model for the conditional mean of a response given a set of regressors. A subset of the regressors may be missing for some study subjects either by design or happenstance. In this article we propose a new class of semiparametric estimators, based on inverse probability weighted estimating equations, that are consistent for parameter vector α0 of the conditional mean model when the data are missing at random in the sense of Rubin…

重要性加权的贝叶斯边际后验密度估计AI 解读

Markov chain sampling schemes generate dependent observations {Θi, 0 ≤ i ≤ n} from a full joint posterior distribution π(θdata). Frequently, only certain marginals of this full posterior density are of interest; thus an interesting problem is how to estimate the marginal posterior densities based on the dependent observations {Θi, 0 ≤ i ≤ n} from π(θ data). We propose a new importance-weighted marginal density estimation (IWMDE) method. An IWMDE is obtained by averaging many…

用多重插补评估血压的长期趋势AI 解读

The National Center for Health Statistics makes available data from three national health evaluation surveys that it has conducted since 1960: NHES I (1960-1962), NHANES I (1971-1975), and NHANES II (1976-1980). There has been considerable interest in using these data to assess secular trends in cardiovascular risk factors such as blood pressure (BP). Unfortunately, underlying trends in BP are confounded with trends in physician treatment of hypertension over the same…

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Bootstrap：统计推断的非参数方法AI 解读

PART ONE: INTRODUCTION Traditional Parametric Statistical Inference Bootstrap Statistical Inference Bootstrapping a Regression Model Theoretical Justification The Jackknife Monte Carlo Evaluation of the Bootstrap PART TWO: STATISTICAL INFERENCE USING THE BOOTSTRAP Bias Estimation Bootstrap Confidence Intervals PART THREE: APPLICATIONS OF BOOTSTRAP CONFIDENCE INTERVALS Confidence Intervals for Statistics With Unknown Sampling Distributions Inference When Traditional…

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计量经济学中的估计与推断AI 解读

Davidson and MacKinnon have written an outstanding textbook for graduates in econometrics, covering both basic and advanced topics and using geometrical proofs throughout for clarity of exposition. The book offers a unified theoretical perspective, and emphasizes the practical applications of modern theory.

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