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高频购买品类的消费者行为：含异质性的风险率模型AI 解读

We apply hazard function models to marketing data on household purchases of disposable diapers to calibrate repeat-purchase and brand-switching behaviors. In the model we allow for household-specific unobserved traits. Hazard function models with fixed-effects heterogeneity specification are computationally feasible. We directly compare the results of fixed- and random-effects heterogeneity specifications in the context of parametric and nonparametric duration-dependence…

点过程现时状态数据的分析AI 解读

This article considers the analysis of event count data in which each subject is observed at only one time point and no information is available on subjects between their entry time and observation points. This type of data, often referred to as current status data, arises frequently—for example, in demography, epidemiology, and reliability studies. Statistical methods for the analysis of current status data from point processes are proposed. Specifically, a statistic for…

小区域估计的拟经验贝叶斯方法AI 解读

This article develops an empirical Bayes-type approach for small area estimation based only on the specification of a set of conditionally independent hierarchical mean and variance functions describing the first two moments of the process generating the data. The objective of the analysis is to draw inference about the intermediate or the random means. We combine the quasi-likelihood functions to construct the quasi-posterior density of the random means conditional on the…

无信息先验与干扰参数AI 解读

We study the conflict between priors that are noninformative for a parameter of interest versus priors that are noninformative for the whole parameter. Our investigation leads us to maximize a functional that has two terms: an asymptotic approximation to a standardized expected Kullback-Leibler distance between the marginal prior and marginal posterior for a parameter of interest, and a penalty term measuring the distance of the prior from the Jeffreys prior. A positive…

Poly-Weibull 分布的贝叶斯分析AI 解读

In this article Bayesian analysis for a Poly-Weibull distribution using informative priors is discussed. This distribution typically arises when the data is the minimum of several Weibull failure times from competing risks. To perform the Bayesian computations, simulation using the Gibbs sampler is suggested. This can be used to find posterior moments, the marginal posterior probability density function, and the predictive risk or reliability.

面向他人分析的最优实验设计AI 解读

We consider the optimal design of experiments in which estimation and design are performed by different parties. The parties are assumed to share similar goals, as reflected by a common loss function, but they may have different prior beliefs. After presenting a few motivating examples, we examine the problem of optimal sample size selection under a normal likelihood with constant cost per observation. We also consider the problem of optimal allocation for given overall…

两阶段整群抽样回归分析中的广义最小二乘 F 检验AI 解读

When data are obtained by two-stage cluster sampling, serious problems can arise if conventional methods that ignore the intracluster correlations are used. Wu, Holt, and Holmes showed that the standard F statistic in regression analysis leads to inflated type I error rate (or size) due to correlated errors in the regression model appropriate for clustered data. They proposed a simple correction to the standard F statistic that takes into account common intracluster…

检验顺序约束均值齐性的简便方法AI 解读

The likelihood-ratio test for equality of partially ordered means, first proposed by Bartholomew, is known to possess power characteristics that are generally superior to those of competing procedures. A limitation of this test, however, is that the null distribution of the test statistic is heavily dependent on both the specific form of the order restriction and the group sample sizes. It is not readily available for most orderings, especially when the group sample sizes…

多维符号检验：基于数据点云几何的推断AI 解读

Multivariate sign tests attracted several statisticians in the past, and it is evident from recent nonparametric literature that they still continue to draw attention. One of the most important features of the univariate sign test is that it does not involve much technical assumptions or complicacy, and this makes it quite popular among statistics users. In this article we have come up with a new method for constructing multivariate sign tests that have reasonable…

协变量测量不完整时的Cox回归AI 解读

This article provides a general solution to the problem of missing covariate data under the Cox regression model. The estimating function for the vector of regression parameters is an approximation to the partial likelihood score function with full covariate measurements and reduces to the pseudolikelihood score function of Self and Prentice in the special setting of case-cohort designs. The resulting parameter estimator is consistent and asymptotically normal with a…

Cox模型中随协变量变化的中位生存时间置信带AI 解读

Let ξp (x) be the pth quantile of the distribution of the life length of an individual with covariate vector x in the Cox model. We introduce an estimator ξp (x) of ξp (x) and develop several families of confidence bands for ξ(x) as a function of x. To construct one type of band, we proceed as follows. We show that as n → ∞, where n is the number of individuals in the study, ) converges weakly to a Gaussian process W(x) with a complicated covariance structure. We then…

利用提名样本估计分布函数AI 解读

A nomination sample consists of independently distributed maxima from subsamples of a population with the same underlying distribution. Nomination sampling occurs when only the item with largest value is chosen from each of n independent subsamples. If the subsamples differ in size, then these observed order statistics are not identically distributed, so estimation schemes built on assumptions of independently and identically distributed (iid) data are most likely…

核回归估计的局部自适应带宽选择AI 解读

Kernel estimators with a global bandwidth are commonly used to estimate regression functions. On the other hand, it is obvious that the choice of a local bandwidth can lead to better results, because a larger class of kernel estimators is available. Evidently, this may in turn affect variability. The optimal bandwidths depend essentially on the regression function itself and on the residual variance, and it is desirable to estimate them from the data. In this article, a…

非参数回归中的置信带AI 解读

New bias-corrected confidence bands are proposed for nonparametric kernal regression. These bands are constructed using only a kernel estimator of the regression curve and its data-selected bandwidth. They are shown to have asymptotically correct coverage properties and to behave well in a small-sample study. One consequence of the large-sample developments is that Bonferroni-type bands for the regression curve at the design points also have conservative asymptotic coverage…

中位绝对偏差的替代尺度估计量AI 解读

In robust estimation one frequently needs an initial or auxiliary estimate of scale. For this one usually takes the median absolute deviation MAD n = 1.4826 med, {|xi − med j x j |}, because it has a simple explicit formula, needs little computation time, and is very robust as witnessed by its bounded influence function and its 50% breakdown point. But there is still room for improvement in two areas: the fact that MAD n is aimed at symmetric distributions and its low (37%)…

线性模型中多个离群点的识别程序AI 解读

We consider the problem of identifying and testing multiple outliers in linear models. The available outlier identification methods often do not succeed in detecting multiple outliers because they are affected by the observations they are supposed to identify. We introduce two test procedures for the detection of multiple outliers that appear to be less sensitive to this problem. Both procedures attempt to separate the data into a set of “clean” data points and a set of…

基于稳健估计的残差：使用与解释AI 解读

Residual plots and diagnostic techniques are important tools for examining the fit of a regression model. In the case of least squares fits, plots of residuals provide a visual assessment of the adequacy of various aspects of the fitted model. An important question is whether plots of robust residuals can be interpreted in the same manner as their least squares counterparts. This article addresses this problem for two popular classes of robust estimates: M estimates and GM…

观察性研究中处理效应的Hodges–Lehmann点估计AI 解读

A Hodges-Lehmann point estimate of an additive treatment effect is a robust estimate derived from the randomization distribution of a rank test. This article shows how to carry out a sensitivity analysis for such an estimate in an observational study where treatments are not randomly assigned. Two cases are discussed in detail: matched pairs and the comparison of two unmatched groups. The method uses a model for the distribution of treatment assignments when hidden biases…

基于回访次数加权修正调查中的不在场偏差AI 解读

When respondents to sample surveys differ from nonrespondents, bias can result. Nonresponse is produced by both refusal and nonavailability. Here we concentrate on nonavailability. Clever weighting schemes to deal with nonavailability bias were proposed about 40 years ago by Politz and Simmons and by Simmons, but further theoretical development has been limited. In the meantime, not only have in-person surveys continued to flourish, but telephone surveys also have become…

棒球连续安打现象的统计分析AI 解读

This article presents a study of hitting streaks for individual batters in the game of baseball. All baseball fans know that players go through periods where they never seem to make an out and other periods where nothing will get them to base. There is no doubt that “hot streaks” and “cold streaks” do occur. The question explored here is whether these streaks occur more (or less) frequently than would be predicted by a probabilistic model of randomness. I examined the…

随机过程探索AI 解读

pro basketball player, occasional software engineer, talent agent, budding television star, world traveller, nemesis of the street gang called the Mutant Creepazoids, theatre patron, supporter of precise and elegant use of the English language, supporter of the war on drugs, unsung hero of the fairy tale Sleeping Beauty, and the target of a vendetta by the local chapter of the Young Republicans.Harry and his

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摘要暂缺

Marshall–Olkin 二元指数分布的扩展AI 解读

This article extends Marshall and Olkin's bivariate exponential distribution such that it is absolutely continuous and need not be memoryless. The new marginal distribution has an increasing failure rate, and the joint distribution exhibits an aging pattern. It offers an advantage in separately identifying the shock arrival rates and their impacts. Regarding estimation of the model, both maximum likelihood and method-of-moments-type estimation are considered. The former is…