非参数回归模型异方差的小波检验

在非参数回归模型的讨论中, 通常假定方差具有齐性结构. 然而事前并不能保证方差齐性. 因此需要检验异方差性. 基于小波方法提出了一种相合的非参数异方差检验. 首先定义了回归模型的条件方差函数的经验小波系数, 然后证明了其渐近正态性. 在此基础上, 利用 Fan 的小波收缩的概念, 提出了异方差性检验的统计量. 模拟结果表明, 本检验方法优于传统的非参数检验方法.     

非参数自回归模型异方差的小波检验

本文讨论了非参数自回归模型异方差的检验问题.在非参数自回归模型的建模过程中,通常假定方差为常数.然而在建模前,我们应该首先检验这-假定是否成立.本文将利用小波方法来检验异方差问题.我们首先利用核估计方法定义经验小波系数,然后讨论其渐近性质.在此基础上,我们提出了异方差性检验的统计量.数值模拟结果表明,我们的方法表现良好.     

半参数随机效应模型的异方差检验

在许多实际问题中,检验观察数据是否出现异方差性是一个相当感兴趣的问题.该文研究了半参数随机效应模型的异方差检验问题.基于Lin(1997)的方法,得到了检验方差成分都为零的Score检验统计量.通过随机模拟和实际数值例子,论证了方法的有效性.利用现有的统计软件,容易实现该文所提出的检验方法.     

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.     

单指标模型异方差检验（英文）

在可加回归模型中,高维回归分析一般采用单指标模型.该模型与参数模型相比更加灵活,同时避免了维数灾难,因为单指标将标准变量向量的维数降低为单变量指标.本文构建了一个带有函数型误差项的单指数回归模型用于检验单指标模型的异方差性.由于回归模型的有效推断要求在存在异方差的情况下考虑异方差,本文提出了检验单指标模型方差不变性的假设.将Levene检验和无限因子水平的方差分析理论结合得到检验统计量用来评估方差同质性.模拟研究显示与已有方法相比,所提检验统计量适用于多种情形.最后将本文的方法应用于分析一组实际数据.     

连续型半参数广义线性纵向数据模型的方差成分检验

回归模型的方差成分检验是一个非常重要的问题.该文针对离差参数的变异, 随机效应的影响及两者同时具有的三种情形, 研究了基于纵向数据的连续型半参数广义线性模型的方差成分检验, 得到了Score检验统计量, 最后通过计算机模拟验证了该文所提出的方法的有效性.     

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.     

单指标回归模型的若干检验问题

在参数和非参数回归模型中,关于异方差检验、一阶自相关存在性检验以及附加变量检验问题都有很多的研究.文中利用P-样条方法,研究了单指标模型的异方差、一阶自相关存在性及附加变量检验问题,分别得到了三种情况下的Score检验统计量,最后给出计算机模拟和实际例子,证实了文中所提出的方法的可行性和有效性,推广和发展了先前的工作.     

随机权函数半参数回归模型的导方差统计分析

在回归分析中,观测值的方差齐性只是一个基本的假定,在参数、半参数和非参数回归模型中关于异方差检验和估计问题已有很多研究.本文在冉昊和朱忠义(2004)讨论的半参数回归模型的基础上,用随机参数方法,讨论随机权函数半参数回归模型中的异方差检验问题,得到了方差齐性检验Score统计量,同时,当半参数模型存在异方差时,本文还给出了估计方差的方法.     

非参数回归模型均值与方差双重变点的估计

本文基于核估计和小波方法研究异方差非参数回归模型中均值函数和方差函数均存在变点的估计问题.首先,构造基于均值函数的核估计量,求出均值变点位置及跳跃度的估计.其次,利用小波方法构造方差变点的估计量,运用该估计量获得方差变点位置与跳跃度的估计,给出变点估计量的渐近性质.最后数值模拟并通过比较验证了方法的有效性.     

Statistical inference of partially linear regression models with heteroscedastic errors

The authors study a heteroscedastic partially linear regression model and develop an inferential procedure for it. This includes a test of heteroscedasticity, a two-step estimator of the heteroscedastic variance function, semiparametric generalized least-squares estimators of the parametric and nonparametric components of the model, and a bootstrap goodness of fit test to see whether the nonparametric component can be parametrized.     

Testing heteroscedasticity in nonparametric regression models based on residual analysis

The importance of detecting heteroscedasticity in regression analysis is widely recognized because efficient inference for the regression function requires that heteroscedasticity should be taken into account. In this paper, a simple test for heteroscedasticity is proposed in nonparametric regression based on residual analysis. Furthermore, some simulations with a comparison with Dette and Munk＇s method are conducted to evaluate the performance of the proposed test. The results demonstrate that the method in this paper performs quite satisfactorily and is much more powerful than Dette and Munk＇s method in some cases.     

TESTING OF CORRELATION AND HETEROSCEDASTICITY IN NONLINEAR REGRESSION MODELS WITH DBL(p,q,1) RANDOM ERRORS

Chaos theory has taught us that a system which has both nonlinearity and random input will most likely produce irregular data. If random errors are irregular data, then random error process will raise nonlinearity (Kantz and Schreiber (1997)). Tsai (1986) introduced a composite test for autocorrelation and heteroscedasticity in linear models with AR(1) errors. Liu (2003) introduced a composite test for correlation and heteroscedasticity in nonlinear models with DBL(p, 0, 1) errors. Therefore, the important problems in regres- sion model are detections of bilinearity, correlation and heteroscedasticity. In this article, the authors discuss more general case of nonlinear models with DBL(p, q, 1) random errors by score test. Several statistics for the test of bilinearity, correlation, and heteroscedas-ticity are obtained, and expressed in simple matrix formulas. The results of regression models with linear errors are extended to those with bilinear errors. The simulation study is carried out to investigate the powers of the test statistics. All results of this article extend and develop results of Tsai (1986), Wei, et al (1995), and Liu, et al (2003).     

Testing heteroscedasticity by wavelets in a nonparametric regression model

In the nonparametric regression models, a homoscedastic structure is usually assumed. However, the homoscedasticity cannot be guaranteed a priori. Hence, testing the heteroscedasticity is needed. In this paper we propose a consistent nonparametric test for heteroscedasticity, based on wavelets. The empirical wavelet coefficients of the conditional variance in a regression model are defined first. Then they are shown to be asymptotically normal, based on which a test statistic for the heteroscedasticity is constructed by using Fan's wavelet thresholding idea. Simulations show that our test is superior to the traditional nonparametric test.     

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??In the additive regression models, the single-index model is considered commonly for high dimensional regression analysis. The specification of this model that it is more flexible compared with a parametric model, and it avoids the curse of dimensionality because the single-index reduces the dimensionality of a standard variable vector (x in the multi-regression) to a univariate index (\beta^\T X in the single-index model). In this paper, we developed a single-index regression model with a functional errors' term that serves in checking the heteroscedasticity. Since the efficient inference of a regression model demands that heteroscedasticity is regarded when it exists, this paper presents the assumptions of testing variance constancy in single-index models. The test statistic is assessing the variance homogeneity stated as a combination of Levene's test and the theories of ANOVA for the infinite factor levels. The test statistic in the simulation studies displays appropriately in all situations compared to a well-known method and applies to a real dataset.     

Testing the Heteroscedasticity in Single-Index Model

In the additive regression models, the single-index model is considered commonly for high dimensional regression analysis. The specification of this model that it is more flexible compared with a parametric model, and it avoids the curse of dimensionality because the single-index reduces the dimensionality of a standard variable vector (x in the multi-regression) to a univariate index (\beta^\T X in the single-index model). In this paper, we developed a single-index regression model with a functional errors' term that serves in checking the heteroscedasticity. Since the efficient inference of a regression model demands that heteroscedasticity is regarded when it exists, this paper presents the assumptions of testing variance constancy in single-index models. The test statistic is assessing the variance homogeneity stated as a combination of Levene's test and the theories of ANOVA for the infinite factor levels. The test statistic in the simulation studies displays appropriately in all situations compared to a well-known method and applies to a real dataset.     

Variance component testing in semiparametric mixed models

It is of considerable interest to test for heteroscedasticity in statistical studies. In this paper, we investigate such a problem under the framework of a semiparametric mixed model. A score test is proposed for the hypothesis that all the variance components are zero. We establish the asymptotic property of the test, and examine its performance in a simulation study. The test is illustrated with the analysis of a longitudinal study of measurements of serum creatinine.     

门限自回归模型条件异方差的Kolmogorov-Smirnov检验

门限自回归模型被广泛地用于许多领域，当建立或使用这类模型时，一个重要问题是需要知道是否存在条件异方差。在本文中，我们对这个问题提出一个非参数检验，检验的大样本理论被给出，我们还通过数值模拟研究了检验方法的有限样本性质。结果表示检验有好的功效。经验百分位点还被给出。