A comparison of asymptotic covariance matrices of three consistent estimators in the Poisson regression model with measurement errors

We consider a Poisson model, where the mean depends on certain covariates in a log-linear way with unknown regression parameters. Some or all of the covariates are measured with errors. The covariates as well as the measurement errors are both jointly normally distributed, and the error covariance matrix is supposed to be known. Three consistent estimators of the parameters—the corrected score, a structural, and the quasi-score estimators—are compared to each other with regard to their relative (asymptotic) efficiencies. The paper extends an earlier result for a scalar covariate.     

一种对称损失函数下刻度参数的最优同变估计

本文研究刻度参数分布族(1/σ)f(x/σ)中刻度参数在损失函数L(σ,δ)=(σ-δ)~2/σδ下的最小风险同变估计及其最小最大性。     

Computational Methods for Semiparametric Linear Regression with Censored Data

Abstract

Semiparametric linear regression with censored data assumes a linear relationship between failure time and covariates without specifying the distributional form of the error term. This approach has attracted considerable attention recently. Most notably, rank regression methods have been derived for parameter estimation, hypothesis testing, and goodness-of-fit analysis. The implementation of these methods requires minimizing discrete objective functions with multiple local minima. Conventional optimization algorithms cannot be used to solve such minimization problems. We develop computational methods to implement rank regression procedures using simulated annealing. Two real data sets are used for illustration. Applications of the new algorithms to the modified least squares estimator of Buckley and James and several other related problems are also described.     

A Subsampling Method for the Computation of Multivariate Estimators with High Breakdown Point

Abstract

All known robust location and scale estimators with high breakdown point for multivariate samples are very expensive to compute. In practice, this computation has to be carried out using an approximate subsampling procedure. In this article we describe an alternative subsampling scheme, applicable to both the Stahel-Donoho estimator and the minimum volume ellipsoid estimator, with the property that the number of subsamples required can be substantially reduced with respect to the standard subsampling procedures used in both cases. We also discuss some bias and variability properties of the estimator obtained from the proposed subsampling process.     

Nonparametric Comparison of Multiple Regression Curves in Scale-Space

This article concerns testing the equality of multiple curves in a nonparametric regression context. The proposed test forms an ANOVA type test statistic based on kernel smoothing and examines the ratio of between- and within-group variations. The empirical distribution of the test statistic is derived using a permutation test. Unlike traditional kernel smoothing approaches, the test is conducted in scale-space so that it does not require the selection of an optimal smoothing level, but instead considers a wide range of scales. The proposed method also visualizes its testing results as a color map and graphically summarizes the statistical differences between curves across multiple locations and scales. A numerical study using simulated and real examples is conducted to demonstrate the finite sample performance of the proposed method.     

A New,Fast Algorithm to Find the Regions of Possible Support for Bivariate Interval-Censored Data

The estimation of the nonparametric maximum likelihood estimate (NPMLE) of the bivariate distribution function on interval-censored data is a recent topic of research. Among other things, it provides a basic tool for checking a parametric model for the bivariate failure times. As a first step in the estimation of the NPMLE for bivariate interval-censored data, the regions of possible support—that is, the rectangles with nonzero mass—are calculated. For this step a new, fast algorithm is introduced here and compared with two existing algorithms. The advantages of our algorithm will be illustrated on the emergence times of permanent teeth on data from the longitudinal Signal® Tandmobiel study.     

Conditional Logistic Regression With Longitudinal Follow-up and Individual-Level Random Coefficients: A Stable and Efficient Two-Step Estimation Method

The analysis of data generated by animal habitat selection studies, by family studies of genetic diseases, or by longitudinal follow-up of households often involves fitting a mixed conditional logistic regression model to longitudinal data composed of clusters of matched case-control strata. The estimation of model parameters by maximum likelihood is especially difficult when the number of cases per stratum is greater than one. In this case, the denominator of each cluster contribution to the conditional likelihood involves a complex integral in high dimension, which leads to convergence problems in the numerical maximization. In this article we show how these computational complexities can be bypassed using a global two-step analysis for nonlinear mixed effects models. The first step estimates the cluster-specific parameters and can be achieved with standard statistical methods and software based on maximum likelihood for independent data. The second step uses the EM-algorithm in conjunction with conditional restricted maximum likelihood to estimate the population parameters. We use simulations to demonstrate that the method works well when the analysis is based on a large number of strata per cluster, as in many ecological studies. We apply the proposed two-step approach to evaluate habitat selection by pairs of bison roaming freely in their natural environment. This article has supplementary material online.     

The precise asymptotic behavior of parameter estimators in Ornstein-Uhlenbeck process

In the present paper, we study the asymptotic behavior for estimator of the drift parameter in an Ornstein-Uhlenbeck process. The Lr-convergence rate and the precise asymptotics in the law of iterated logarithm and in the law of logarithm for the estimator are obtained. Moreover, we also get the complete moment convergence of this estimator. The main method of this paper is the deviation inequality for the quadratic functional.     

一类纵向数据半参数模型估计的收敛速度

本文研究了一类纵向数据半参数模型参数和回归函数的估计问题.利用最小二乘法和一般的非参数权函数方法,获得了参数估计量的强收敛速度和回归函数估计量的一致收敛速度,推广了文献[4]的相应结果.     

基于边缘ZI回归模型的分组数据影响分析

为了研究含零较多的分组计数数据对边缘ZI(zero-inflated)回归模型的影响,在完全数据的对数似然基础上利用局部影响法对其进行诊断.同时,基于模型中参数的ES(expectation-solution)估计,分别研究了类内加权扰动、类音加权扰动、解释变量扰动和响应变量扰动下的局部影响分析,得到了相应的诊断统计量.最后,根据所得统计量,获得了园艺试验中一组计数数据的影响点,结果说明该文提出的方法是有效的.