高维异方差高斯混合罚模型聚类

罚模型聚类实现了在聚类过程中精简变量的目标,同时如何识别聚类的有效变量成了一个新的问题.在这个问题上,已有的研究有成对罚模型,模型处理了各类数据同方差的情况.考察了异方差情况下的变量选择问题,针对异方差数据提出了两种新的模型,并给出模型的解和算法.模拟数据分析结果表明,异方差数据上两个新模型都有更好的表现.     

面板数据交互固定效应模型的方差分量检验

研究了面板数据交互固定效应模型中方差分量的检验问题.首先依据模型中误差项的估计构造辅助回归模型,然后根据该辅助回归构造检验统计量,对模型中的异方差性进行检验.进一步,通过构造不同的辅助回归模型和检验统计量可以判别异方差的来源.在一定正则条件下,得到了检验统计量在原假设和备择假设下的渐近分布,并说明所提出的检验方法不依赖于误差分布.最后,通过模拟研究对本文的检验方法进行评价,说明所提检验方法是有效的.     

线性约束下异方差回归模型参数的极大似然估计

运用参数的极大似然估计法,给出在线性约束条件Hβ=C下异方差回归模型参数β和λ的极大似然估计,并讨论了估计参数的性质和模型的残差.利用得到的结论对线性约束下异方差回归模型的进一步研究和应用具有一定的理论和实际价值.     

部分线性自回归模型中误差方差的核估计

基于非参数函数的核估计,构造了部分线性自回归模型中误差四阶矩的相合估计,从而给出了误差方差核估计的渐近正态性,并通过模拟算例和实例说明了其应用.     

拟线性回归预测模型的稳定最小二乘解

可线性化回归预测模型通过换元进行线性回归,换元前后的因变量具有异方差性,致使拟线性回归参数的精度较低.运用GL算法给出了此类模型的稳定最小二乘解,提高了参数的估计精度,最后给出了一个应用实例.     

PLM中误差方差未知时的GLR

本文检验部分线性回归模型(PLM)中,误差的方差未知时,函数部分是否是线性函数,在备择假设下,先用局部多项式方法估计出函数部分,再估计参数部分.计算出了零假设下广义似然比(GLR)检验统计量的表达式,给出了它的渐近分布,并对结果进行了模拟.     

基于异方差的自回归预测模型的参数估计及其应用

从齐性方差的线性回归模型参数估计的最小二乘法出发,通过对统计资料的适当变换,利用加权最小二乘法,获得了异方差的线性自回归模型和四种异方差的非线性自回归模型的参数估计公式,并举例阐述了估计公式的应用.     

半参数回归模型的异方差统计分析

在回归分析中，方差齐性的假设是一个普遍关心的问题．在参数和非参数回归模型中，关于异方差检验问题已经有很多的研究，见(【1】，【4】，【7】)．本文研究了半参数回归模型的异方差检验问题，得到了方差齐性检验的SCORE统计量，证明了该统计量的渐近x^2性质，最后给出计算机模拟和实际例子，推广和发展了Eubank和Thomas(1993)，韦博成(1995)的工作．     

随机权函数非线性回归模型的异方差统计分析

在回归分析中，随机误差是否存在方差齐性是理论与实际工作者都十分关心的问题，方差齐性假设并不总是正确的，在线性和非线性回归中关于异方差的诊断问题已有许多讨论（[1],[2],[4],[5]）。本文在韦博成（1995）讨论了加权非线性回归模型的基础上，用随机系数的方法，讨论随机权函数非线性回归模型中的异方差检验问题，得到了方差齐性检验的似然比统计量和score统计量，同时，当模型存在异方差时，本文给出了估计方差的一种方法。     

具有线性趋势回归信度模型异方差的score检验

回归信度模型在保险研究中具有重要的作用.本文分险种内部,险种之间,险种内部及之间三种情形讨论了具有线性趋势回归信度模型异方差的score检验问题.首先推导了异方差存在性检验的score检验统计量,然后利用Monte-Carlo方法模拟了这几种检验统计量的功效,功效模拟结果显示：这几种检验统计量都有很好的检验效果.最后利用文中所得到的检验方法对旅客意外身体伤害保险数据进行了实例分析.     

线性回归模型中方差变点的连续监测

The paper investigates the sequential observations’ variance change in linear regression model. The procedure is based on a detection function constructed by residual squares of CUSUM and a boundary function which is designed so that the test has a small probability of false alarm and asymptotic power one. Simulation results show our monitoring procedure performs well when variance change occurs shortly after the monitoring time. The method is still feasible for regression coefficients change or both variance and regression coefficients change problem.     

Heteroscedasticity check in nonlinear semiparametric models based on nonparametric variance function

The assumption of homoscedasticity has received much attention in classical analysis of regression. Heteroscedasticity tests have been well studied in parametric and nonparametric regressions. The aim of this paper is to present a test of heteroscedasticity for nonlinear semiparametric regression models with nonparametric variance function. The validity of the proposed test is illustrated by two simulated examples and a real data example.     

A Goodness-of-Fit Test for the Functional Linear Model with Scalar Response

This article proposes a goodness-of-fit test for the null hypothesis of a functional linear model with scalar response. The test is based on a generalization to the functional framework of a previous one, designed for the goodness-of-fit of regression models with multivariate covariates using random projections. The test statistic is easy to compute using geometrical and matrix arguments, and simple to calibrate in its distribution by a wild bootstrap on the residuals. The finite sample properties of the test are illustrated by a simulation study for several types of basis and under different alternatives. Finally, the test is applied to two datasets for checking the assumption of the functional linear model and a graphical tool is introduced. Supplementary materials are available online.     

随机设计下非参数回归模型方差变点Ratio检验

研究随机设计下非参数回归模型方差变点Ratio检验.首先用局部多项式方法估计回归曲线得到残差序列,其次基于残差的平方序列构造Ratio检验统计量并推导检验统计量的极限分布.最后数值模拟与实例分析结果表明方法的有效性.     

Empirical likelihood analysis of the Buckley-James estimator

The censored linear regression model, also referred to as the accelerated failure time (AFT) model when the logarithm of the survival time is used as the response variable, is widely seen as an alternative to the popular Cox model when the assumption of proportional hazards is questionable. Buckley and James [Linear regression with censored data, Biometrika 66 (1979) 429-436] extended the least squares estimator to the semiparametric censored linear regression model in which the error distribution is completely unspecified. The Buckley-James estimator performs well in many simulation studies and examples. The direct interpretation of the AFT model is also more attractive than the Cox model, as Cox has pointed out, in practical situations. However, the application of the Buckley-James estimation was limited in practice mainly due to its illusive variance. In this paper, we use the empirical likelihood method to derive a new test and confidence interval based on the Buckley-James estimator of the regression coefficient. A standard chi-square distribution is used to calculate the P-value and the confidence interval. The proposed empirical likelihood method does not involve variance estimation. It also shows much better small sample performance than some existing methods in our simulation studies.     

基于最小二乘近似的模型平均方法

本文提出基于最小二乘近似的模型平均方法.该方法可用于线性模型、广义线性模型和分位数回归等各种常用模型.特别地,经典的Mallows模型平均方法是该方法的特例.现存的模型平均文献中,渐近分布的证明一般需要局部误设定假设,所得的极限分布的形式也比较复杂.本文将在不使用局部误设定假设的情形下证明该方法的渐近正态性.另外,本文将该方法发展到维数发散的情形.数值结果显示了该方法的优势.     

Spline-based sieve maximum likelihood estimation in the partly linear model under monotonicity constraints

We study a spline-based likelihood method for the partly linear model with monotonicity constraints. We use monotone B-splines to approximate the monotone nonparametric function and apply the generalized Rosen algorithm to compute the estimators jointly. We show that the spline estimator of the nonparametric component achieves the possible optimal rate of convergence under the smooth assumption and that the estimator of the regression parameter is asymptotically normal and efficient. Moreover, a spline-based semiparametric likelihood ratio test is established to make inference of the regression parameter. Also an observed profile information method to consistently estimate the standard error of the spline estimator of the regression parameter is proposed. A simulation study is conducted to evaluate the finite sample performance of the proposed method. The method is illustrated by an air pollution study.     

Testing for the Absence of Random Effects in a Two-way Nested Design with Mixed Effects Model: A Nonparametric Approach

Two-way nested design with mixed effects model arises in many practical situations. In the classical analysis of variance set-up, a test for the absence of the random effects is obtained under the assumption that the random effects and the errors are normally distributed. The present paper avoids this assumption and provides an asymptotically distribution-free test procedure for the above problem. The asymptotic null distribution of the test statistic is obtained. Actual implementation of the test is straight forward given the prior information on quantiles of the intra-block differences of observations. In the absence of such information, working test procedures are proposed. The performances of these tests are compared with the classical analysis of variance test through simulations. The tests are then illustrated by some real data sets.     

线性回归模型误差相关的一种诊断方法

本文就线性回归模型的优化问题 ,对误差的自相关性作了一些简单的分析 ,得出了一个对自相关现象的诊断方法 ,从而为模型的进一步诊断和治疗提供了依据和思路