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层级泊松回归建模AI 解读

The Poisson model and analyses here feature nonexchangeable gamma distributions (although exchangeable following a scale transformation) for individual parameters, with standard deviations proportional to means. A relatively uninformative prior distribution for the shrinkage values eliminates the ill behavior of maximum likelihood estimators of the variance components. When tested in simulation studies, the resulting procedure provides better coverage probabilities and…

协变量缺失回归中的加权半参数估计AI 解读

This article investigates estimation of the regression coefficients in an assumed mean function when covariates on some subjects are missing. We examine the performance of a Horvitz and Thompson (1952)-type weighted estimator by using different estimates of the selection probabilities, which may be treated as nuisance parameters (or a nuisance function). In particular, we investigate the properties of the estimate of the regression parameters when the selection probabilities…

Cox–Ingersoll–Ross 模型的参数估计AI 解读

The Cox-Ingersoll-Ross model is a diffusion process suitable for modeling the term structure of interest rates. In this paper, we consider estimation of the parameters of this process from observations at equidistant time points. We study two estimators based on conditional least squares as well as a one-step improvement of these, two weighted conditional least-squares estimators, and the maximum likelihood estimator. Asymptotic properties of the various estimators are…

条件异方差模型中准极大似然估计量的渐近偏差AI 解读

For conditional heteroskedasticity models, the authors study the identification condition that is required for consistency of a non-Gaussian quasi-maximum-likelihood estimator. They show that, if the conditional mean is zero or if a symmetry condition is satisfied, then the identification condition is satisfied. Without symmetry, an additional parameter, for the location of the innovation density, must be added for identification. For the conditional variance parameters of a…

弱工具变量下的工具变量回归AI 解读

This paper develops asymptotic distribution theory for instrumental variables regression when the partial correlations between the instruments and the endogenous variables are weak, here modeled as local to zero. Asymptotic representation are provided for various statistics, including two-stage least squares and limited information maximum likelihood estimators, Wald statistics, and statistics testing overidentification and endogeneity. The asymptotic distributions provide…

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受约束协方差分量模型中的估计与检验AI 解读

A cutting plane algorithm is proposed for estimating variance and covariance components by maximum likelihood or restricted maximum likelihood enforcing the constraints that covariance matrices be positive semidefinite. For tests of hypotheses involving these constrained estimates, an asymptotic parametric bootstrap is proposed for approximating the distribution of the likelihood ratio test statistic. Although the bootstrap is generally inconsistent when the true parameter…

病例对照数据回归模型的最大似然拟合AI 解读

We consider fitting categorical regression models to data obtained by either stratified or nonstratified case-control, or response selective, sampling from a finite population with known population totals in each response category. With certain models, such as the logistic with appropriate constant terms, a method variously known as conditional maximum likelihood (Breslow & Cain, 1988) or pseudo-conditional likelihood (Wild, 1991), which involves the prospective fitting of a…

一种多元条件异方差模型AI 解读

Tsay (1987) developed the conditional heteroscedastic autoregressive moving-average model, which includes the conditional heteroscedastic autoregressive and random coefficient autoregressive models as special cases. This paper establishes the multivariate conditional heteroscedastic autoregressive moving-average model, and considers its theoretical properties and applications. Maximum likelihood estimation of the model is discussed in detail. A representation of the…

用最小卡方方法高效估计随机微分方程AI 解读

We propose a minimum chi-squared estimator for the parameters of an ergodic system of stochastic differential equations with partially observed state. We prove that the efficiency of the estimator approaches that of maximum likelihood as the number of moment functions entering the chi-squared criterion increases and as the number of past observations entering each moment function increases. The rninimised criterion is asymp totically chi-squared and can be used to test…

多个数据集共同线性函数关系的估计AI 解读

This paper studies a functional-type linear measurement-error model, in which k data sets of observations are assumed to have in common a set of linear restrictions on their respective unobservable constant vectors. Each data set consists of replicated measurements of each one of several, generally unequal, constant vectors, with normal error assumed independent for each measurement made. The error covariance matrices are unspecified, and are equal for measurements within a…

分组数据的稳健估计AI 解读

Here we investigate the robustness properties of the class of minimum power divergence estimators for grouped data. This class contains the classical maximum likelihood estimators for grouped data. We find that the bias of these estimators due to deviations from the assumed underlying model can be large. Therefore, we propose a more general class of estimators that allows us to construct robust procedures. By analogy with Hampel's theorem, we define optimal bounded influence…

含变点的线性变量误差模型推断AI 解读

A new linear structural errors-in-variables regression with changepoint model is considered. In this model we consider the likelihood ratio test based on the maximum Hotelling T 2 for the test of no change against the alternative of exactly one change. If there is a change, either known a priori or by testing, then we estimate the unknown changepoint parameter and some other related parameters by maximum likelihood. The limiting distribution of the changepoint estimator is…

多分类回归AI 解读

An automatic procedure that uses linear splines and their tensor products is proposed for fitting a regression model to data involving a polychotomous response variable and one or more predictors. The fitted model can be used for multiple classification. The automatic fitting procedure involves maximum likelihood estimation, stepwise addition, stepwise deletion, and model selection by the Akaike information criterion, cross-validation, or an independent test set. A modified…

基于含噪支持函数数据的凸集估计AI 解读

In problems of medical imaging and robotic vision, measurements of a convex set are sometimes obtained via the set's support function. The standard way in which the convex set is recovered from such data is to suppose that it is polygonal, model the errors as Normal random variables, and apply constrained maximum likelihood methods. Typically, the number of sides assumed of the polygon is equal to or a little less than the number of data points. However, from a statistical…

多元二元响应重复测量的模型AI 解读

This article presents a logit model for a vector of binary variables observed for each subject under multiple conditions. The model contains a vector of random effects to account for correlations among the repeated measurements. A nonparametric treatment of the random effects implies a multivariate log-linear model having quasi-symmetric structure for the cross-classification of responses at the various conditions. The fit yields estimates of within-subject effects comparing…

广义线性混合模型的最大似然算法AI 解读

Maximum likelihood algorithms are described for generalized linear mixed models. I show how to construct a Monte Carlo version of the EM algorithm, propose a Monte Carlo Newton-Raphson algorithm, and evaluate and improve the use of importance sampling ideas. Calculation of the maximum likelihood estimates is feasible for a wide variety of problems where they were not previously. I also use the Newton-Raphson algorithm as a framework to compare maximum likelihood to the…

混合线性模型中的有界影响估计AI 解读

Bounded influence estimation (also known as generalized M or GM estimation) in the regression model is reviewed. The definitions of bounded influence estimation proposed by Mallows and Schweppe are then extended to the mixed linear model. This is achieved by applying appropriate weight functions to maximum likelihood and restricted maximum likelihood estimating equations. The asymptotic properties of the new estimators are obtained, and the estimators are applied to an…

分组数据的稳健估计AI 解读

Here we investigate the robustness properties of the class of minimum power divergence estimators for grouped data. This class contains the classical maximum likelihood estimators for grouped data. We find that the bias of these estimators due to deviations from the assumed underlying model can be large. Therefore, we propose a more general class of estimators that allows us to construct robust procedures. By analogy with Hampel's theorem, we define optimal bounded influence…

混合线性模型中的有界影响估计AI 解读

Bounded influence estimation (also known as generalized M or GM estimation) in the regression model is reviewed. The definitions of bounded influence estimation proposed by Mallows and Schweppe are then extended to the mixed linear model. This is achieved by applying appropriate weight functions to maximum likelihood and restricted maximum likelihood estimating equations. The asymptotic properties of the new estimators are obtained, and the estimators are applied to an…

由含噪支持函数数据估计凸集AI 解读

In problems of medical imaging and robotic vision, measurements of a convex set are sometimes obtained via the set's support function. The standard way in which the convex set is recovered from such data is to suppose that it is polygonal, model the errors as Normal random variables, and apply constrained maximum likelihood methods. Typically, the number of sides assumed of the polygon is equal to or a little less than the number of data points. However, from a statistical…

二元数据一般随机效应模型的极大似然一致性AI 解读

We consider a general random effects model for repeated binary measures, assuming a latent linear model with any class of mixing distributions. The latent model is assumed to have the Laird-Ware structure, but the random effects may be from any specified class of multivariate distributions and the error vector may have any specified continuous distribution. Elementwise threshold crossing then gives the observed vector of binary outcomes. Special cases of this model include…

长程依赖的极限理论及相关模型的统计推断AI 解读

This paper provides limit theorems for multivariate, possibly non-Gaussian stationary processes whose spectral density matrices may have singularities not restricted at the origin, applying those limiting results to the asymptotic theory of parameter estimation and testing for statistical models of long-range dependent processes. The central limit theorems are proved based on the assumption that the innovations of the stationary processes satisfy certain mixing conditions…

若干指数型面板模型有效半参数估计的一则注记AI 解读

This paper investigates the semiparametric efficiency of the conditional maximum likelihood estimation in some panel models. The nonparametric component of the model is the unknown distribution of the fixed effect. For the exponential panel model, there exists a complete sufficient statistic for the fixed effect. When the complete sufficient statistic does not depend on the parameter of interest, the conditional maximum likelihood estimator (CMLE) achieves the semiparametric…