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AR(1)误差的线性随机效应模型中方差齐性和自相关性的检验

在回归分析中，方差齐性是一个很基本的假设．本文对具有AR(1)误差的线性随机效应模型，研究了方差齐性和自相关性的检验问题．我们分别讨论了随机误差异方差、随机效应异方差、多元异方差以及自相关性的检验问题，并用score检验方法给出了三种方差齐性和自相关性的检验统计量．随机模拟的结果表明，当样本容量较大时，检验的功效较好．本文还给出一个数值例子说明检验方法的实用性．另外，模型的结果也可以推广到非线性情形．     

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.     

非线性随机效应模型的异方差性检验

随机效应模型广泛应用于刻画重复测量数据的特征．在该模型中,随机误差的方差包括受试群体内部及受试群体之间两项方差．Ｚｈａｎｇ和 Ｗｅｉｓｓ ２０００年研究了线性随机效应模型的异方差检验,本文对非线性随机效应模型,分别讨论了群体内、群体间和多变量的异方差性的检验问题,得到了检验的ｓｃｏｒｅ统计量,并讨论了三种情形下,相应的ｓｃｏｒｅ函数之间的关系．最后给出一个数值例子说明上述方法的有用性．     

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．     

具有ARIMA（0，1，0）对称误差的非线性模型的统计诊断

本文讨论具有ARIMA(0,1,0)对称误差的非线性模型的异方差检验和局部影响分析.对称误差分布族包括正态,t,power exponential,logistics Ⅰ,Ⅱ,污染正态等所有对称连续分布.文章首先导出了关于白噪声异方差检验的score统计量及其调整形式,然后对模型进行了局部影响分析,得到了基于似然函数扰动和反应变量扰动的诊断统计量.最后,利用实际数据说明了检验方法的应用,并用Monte Carlo模拟方法研究了异方差检验统计量的检验功效.     

非线性纵向数据模型中方差和自相关系数的齐性检验

刻画纵向数据的协方差结构有三个可能因素：随机效应、序列相关和随机误差．在纵向数据分析中，模型方差的齐性是一个基本假定．但是，该假设未必正确．Zhang和、Weiss^[1]研究了具有随机效应的线性模型的异方差检验．林金官和韦博成^[2]将Zhang和、Weiss^[1]的结果推广到非线性情形．本文对具有自相关误差的非线性纵向数据模型，研究了方差齐性和相关系数的齐性检验，得到了检验的score统计量并应用于血浆渗透数据(见Davidian和Giltian^[3])．最后，本文还给出了模拟结果．     

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.     

非线性Poisson-Gamma回归模型中存在偏大离差时离差参数的齐性检验

Poisson回归模型广泛地应用于分析计数型数据，但该模型往往存在偏大离差(overdispersion)问题．刻画Poisson回归模型的偏大离差性的两种方法是拟似然方法和随机效应法(Lee＆Nelder，2000)，已有许多作者利用随机效应法研究了Poisson模型的偏大离差的检验问题．但他们均假定随机效应是独立同分布的，本文对他们的假设进行检验．我们分别在组内效应一致和组内效应不一致的情形下，研究了存在偏大离差的Poisson-Gamma非线性随机效应模型中，随机效应方差(称为离差参数)的齐性检验问题，得到了离差参数齐性的score检验统计量．最后给出两个数值例子说明本文方法的应用．     

具有ARIMA(0,1,0)误差的非线性模型的异方差检验

本文讨论随机误差是 ARIMA( 0 ,1 ,0 )序列的非线性回归模型的异方差检验问题 .首先导出了检验的 score统计量 ,然后利用参数的正交变换 ,得到了调整的 score统计量 .最后 ,利用氯化物数据 ( Bates &Watts,1 988)说明了检验方法的应用     

Heteroscedasticity and/or Autocorrelation Checks in Longitudinal Nonlinear Models with Elliptical and AR（1） Errors

The aim of this paper is to study the tests for variance heterogeneity and/or autocorrelation in nonlinear regression models with elliptical and AR(1) errors. The elliptical class includes several symmetric multivariate distributions such as normal, Student-t, power exponential, among others. Several diagnostic tests using score statistics and their adjustment are constructed. The asymptotic properties, including asymptotic chi-square and approximate powers under local alternatives of the score statistics, are studied. The properties of test statistics are investigated through Monte Carlo simulations. A data set previously analyzed under normal errors is reanalyzed under elliptical models to illustrate our test methods.     

具有一致相关的纵向数据模型中方差和相关系数的齐性检验

在纵向数据分析中, 模型方差的齐性是一个基本假定, 但是该假定未必正确. 林金官、韦博成^[1]讨论了具有AR(1)误差的非线性纵向数据模型中方差和相关系数的齐性检验. 本文对具有一致相关协方差结构的纵向数据模型, 研究了方差齐性和相关系数齐性的检验, 得到了检验的score统计量, 并应用于葡萄糖数据. 最后, 本文还给出了模拟结果.     

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.     

Two tests for heteroscedasticity in nonparametric regression

In this paper, two new tests for heteroscedasticity in nonparametric regression are presented and compared. The first of these tests consists in first estimating nonparametrically the unknown conditional variance function and then using a classical least-squares test for a general linear model to test whether this function is a constant. The second test is based on using an overall distance between a nonparametric estimator of the conditional variance function and a parametric estimator of the variance of the model under the assumption of homoscedasticity. A bootstrap algorithm is used to approximate the distribution of this test statistic. Extended versions of both procedures in two directions, first, in the context of dependent data, and second, in the case of testing if the variance function is a polynomial of a certain degree, are also described. A broad simulation study is carried out to illustrate the finite sample performance of both tests when the observations are independent and when they are dependent.     

Practical tests for randomized complete block designs

A class of affine-invariant test statistics, including a sign test and a related family of signed-rank tests, is proposed for randomized complete block designs with one observation per treatment. This class is obtained by using the transformation-retransformation approach of Chakraborty, Chaudhuri and Oja along with a directional transformation due to Tyler. Under the minimal assumption of directional symmetry of the underlying distribution, the null asymptotic distribution of the sign test statistic is shown to be chi-square with p-1 degrees of freedom. The same null distribution is also proved for the family of signed-rank statistics under the assumption of symmetry of the underlying distribution. The Pitman asymptotic relative efficiencies of the tests, relative to Hotelling-Hsu's T² are established. Several score functions are discussed including a simple linear score function and the optimal normal score function. The test based on the linear score function is compared to the other members of this family and other statistics in the literature through efficiency calculations and Monte Carlo simulations. This statistic has an excellent performance over a wide range of distributions and for small as well as large dimensions.     

具有线性趋势回归信度模型的自相关性的score检验

回归信度模型在保险研究中具有重要的作用。本文讨论了具有线性趋势回归信度模型自相关性的score检验问题。首先推导出模型中自相关存在性检验的score检验统计量,然后利用Monte-Carlo方法模拟了此种检验统计量的功效。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。     

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Homogeneity of variance and correlation coefficients is one of assumptions in the analysis of longitudinal data.However, the assumption can be challenged. In this paper, we mainly propose and analyze nonlinear mixed effects models for longitudinal data with exponential correlation covariance structure, intend to introduce Huber's function in the log likelihood function and get robust estimation (M-estimation) by Fisher scoring method. Score test statistics for homogeneity of variance and correlation coefficient based on M-estimation are then studied. A simulation study is carried to assess the performance of test statistics and the method we proposed in the paper is illustrated by an actual data example.