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广义线性模型中参数与半参数设定的检验AI 解读

We consider a generalized partially linear model E(Y|X, T) = G{X T β + m(T)}, where G is a known function, β is an unknown parameter vector, and m is an unknown function. We introduce a test statistic that allows one to decide between a parametric and a semiparametric model: (a) m is linear (i.e., m(t) = t T γ for a parameter vector γ), and (b) m is a smooth (nonlinear) function. Under linearity (a), we show that the test statistic is asymptotically normal. Moreover, we…

模型选择与假设检验的内在极限程序AI 解读

Improper priors typically arise in default Bayesian estimation problems. In the Bayesian approach to model selection or hypothesis testing, the main tool is the Bayes factor. When improper priors for the parameters appearing in the models are used, the Bayes factor is not well defined. The intrinsic Bayes factor introduced by Berger and Pericchi is an interesting method for overcoming that difficulty. That method is of particular interest as a means for generating proper…

异方差与回归模型近似设定下的极小极大稳健设计及权重AI 解读

This article addresses the problem of constructing designs for regression models in the presence of both possible heteroscedasticity and an approximately and possibly incorrectly specified response function. Working with very general models for both types of departure from the classical assumptions, I exhibit minimax designs and correspondingly optimal weights. Simulation studies and a case study accompanying the theoretical results lead to the conclusions that the robust…

单元格含多个计数的双因素计数数据分析AI 解读

Multiple counts may occur in each cell of an a × b two-way layout (balanced or unbalanced) of two fixed factors A and B. Standard log-linear model analysis based on a Poisson distribution assumption of the cell counts is not applicable here, because of the unbalanced nature of the table or because the Poisson distribution assumption is not valid. We develop C(α) tests for interaction and main effects assuming data to be Poisson distributed and also assuming that data within…

纵向数据的非参数回归分析AI 解读

Nonparametric methods are developed for estimating the dose effect when a response consists of correlated observations over time measured in a dose–response experiment. The methods can also be applied to data collected from a completely randomized design experiment. Methods are developed for the detection and description of the effects of dose, time, and their interaction. The methods allow for individual variation in the timing and number of observations. A generalization…

连接函数与方差函数未知时的拟似然回归AI 解读

We consider the multiple regression model E(y) = μ, μ = g(x T β), var(y) — [sgrave]2(μ) with predictors x, link function g, and variance function [sgrave]2(·). The aim is to reduce the assumptions in a fully parametric generalized linear model or a quasi-likelihood model by allowing the link and the variance functions to be unknown but smooth. These functions are then estimated nonparametrically, and the estimates are substituted into the quasi-likelihood function. We…

非可忽略无应答下重复结局的半参数回归AI 解读

We consider inference about the parameter β* indexing the conditional mean of a vector of correlated outcomes given a vector of explanatory variables when some of the outcomes are missing in a subsample of the study and the probability of response depends on both observed and unobserved data values; that is, nonresponse is nonignorable. We propose a class of augmented inverse probability of response weighted estimators that are consistent and asymptotically normal (CAN) for…

多个二乘二表共同优势比的近似精确推断AI 解读

The conditional maximum likelihood estimator (MLE) of the common odds ratio in a sequence of independent 2 × 2 tables is known to be superior to the Mantel–Haenszel estimator in terms of asymptotic efficiency and has the further advantage that its exact distribution is known. However, a long-standing barrier to the widespread use of this estimator has been computational intractability; in particular, the calculation of significance levels, confidence sets, and power based on…

利用历史对照调整二元数据趋势检验中的协变量AI 解读

Historical data often play an important role in helping interpret the results of a current study. This article is motivated primarily by one specific application: the analysis of data from rodent carcinogenicity studies. By proposing a suitable informative prior distribution on the relationship between control outcome data and covariates, we derive modified trend test statistics that incorporate historical control information to adjust for covariate effects. Frequentist and…

数值方法下的贝叶斯经济学：利用先验信息开展计量分析与决策AI 解读

Theory and Basics.- A Quick Course in Bayesian Statistics and Decision Theory.- New Advances in Numerical Bayesian Techniques.- Applications in Econometrics.- Imposing Economic Theory.- Studying Parameters of Interest.- Unit Root and Cointegration Tests.- Model Specification Uncertainty.- Forecasting.- More Realistic Models Through Numerical Methods.- Applications to Economic Decision Making.- Decision Theory Applications.

连续时间马尔可夫链及其应用：奇异摄动方法AI 解读

Applications (1978) 7 Vorob'ev, Game Theory: Lectures for Economists and Systems Scientists (1977) 8 Shiryayev, Optimal Stopping Rules (1978) 9 Ibragimov/Rozanov, Gaussian Random Processes (1978) Wonham, Linear Multivariable Control: A Geometric Approach, Third Ed. (1985) Hida, Brownian Motion (1980) Hestenes, Conjugate Direction Methods in Optimization (1980) Kallianpur, Stochastic Filtering Theory (1980) Krylov, Controlled Diffusion Processes (1980) Prabhu, Stochastic…

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为估计共同成功概率而序贯选择两类实验AI 解读

To estimate a success probability p, two experiments are available: individual Bernoulli (p) trials or the product of τ individual Bernoulli (p) trials. This problem has its roots in reliability where either single components can be tested or a system of τ identical components can be tested. A total of N experiments can be performed, and the problem is to sequentially select some combination (allocation) of these two experiments, along with an estimator of p, to achieve low…

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每格含多个计数的双因素布局分析AI 解读

Multiple counts may occur in each cell of an a × b two-way layout (balanced or unbalanced) of two fixed factors A and B. Standard log-linear model analysis based on a Poisson distribution assumption of the cell counts is not applicable here, because of the unbalanced nature of the table or because the Poisson distribution assumption is not valid. We develop C(α) tests for interaction and main effects assuming data to be Poisson distributed and also assuming that data within…

链接函数与方差函数未知的拟似然回归AI 解读

We consider the multiple regression model E(y) = μ, μ = g(x T β), var(y) — [sgrave]2(μ) with predictors x, link function g, and variance function [sgrave]2(·). The aim is to reduce the assumptions in a fully parametric generalized linear model or a quasi-likelihood model by allowing the link and the variance functions to be unknown but smooth. These functions are then estimated nonparametrically, and the estimates are substituted into the quasi-likelihood function. We…

聚类数据的扩展广义估计方程AI 解读

Typically, analysis of data consisting of multiple observations on a cluster is complicated by within-cluster correlation. Estimating equations for generalized linear modeling of clustered data have recently received much attention. This article proposes an extension to the generalized estimating equation method proposed by Liang and Zeger, which treats within-cluster correlations as nuisance parameters. Using ideas from extended quasi-likelihood, estimating equations for…

正电子发射断层成像及广义反卷积模型的变异评估AI 解读

The problem of variance assessment for positron emission tomography (PET) image reconstructions is considered in the context of generalized deconvolution. A refinement of an approximate technique proposed by Carson and colleagues is examined. Computational implications of representing the reconstruction kernel in terms of a weighted sum of Gaussian densities are developed. Bias and variance characteristics of the resulting variance estimators are examined by numerical…

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逮捕率的层级贝叶斯分析AI 解读

A Bayesian hierarchical model provides the basis for calibrating the crimes avoided by incarceration of individuals convicted of drug offenses compared to those convicted of nondrug offenses. Two methods for constructing reference priors for hierarchical models both lead to the same prior in the final model. We use Markov chain Monte Carlo methods to fit the model to data from a random sample of past arrest records of all felons convicted of drug trafficking, drug…

经济学与计量经济学进展：理论与应用——第七届世界大会AI 解读

presented in the invited symposium of the Seventh World Congress of the Econometric Society. The papers summarize and interpret key recent developments and discuss current and future directions in a wide range of topics in economics and econometrics. They cover both theory and applications. Authored by leading specialists in their fields, these volumes provide a unique survey of progress in the discipline

统计理论与实践的进展：纪念 Samuel Kotz 的文集AI 解读

Partial table of contents: SAMUEL KOTZ. About Sam Kotz (B. Shube). STATISTICS IN THE WORLD. Statistics and Politics (D. Bartholomew). Disperson and Cohesion in the Statistical Profession (Z. Kenessey). MODELS. On Ling's Scaling Law (S. Davies & P. Hall). A Generalization of the Lifetime Pairs of Renewal Theory (F. Steutel & K. van Harn). BIOSTATISTICS. Some Control Methods for Epidemics (D. Daley & J. Gani). TESTING AND ESTIMATION. Some Rank Tests for Multivariate Censored…