具有随机效应和AR(1)误差的非线性纵向数据模型中组间方差和自相关系数的齐性检验

组间方差和自相关系数的齐性是纵向数据分析的基本假设之一,然而这种假设需要进行统计检验. Zhang \&; Weiss$^{[15]}$ 讨论了线性随机效应模型的组间和组内方差齐性的检验问题;林金官 \&; 韦博成$^{[10]}$ 研究了具有AR(1)误差但没有随机效应的非线性模型的自相关系数的齐性检验.该文研究具有随机效应和AR(1)误差的非线性模型的组间方差和自相关系数的齐性检验问题,构造了几个score检验统计量, 并通过Monte Carlo模拟方法研究了检验统计量的性质.最后利用该文的方法分析一组实际数据和一组模拟数据.     

线性回归模型Bootstrap LM-Error检验的水平扭曲

基于OLS估计残差,本文将Bootstrap方法用于空间误差相关性LM-Error检验,综合考虑Bootstrap模拟抽样次数、空间衔接结构以及样本量,研究并比较空间误差相关Bootstrap LM-Error检验与渐近检验的水平扭曲。大量Monte Carlo实验结果显示,当模型误差不满足独立正态分布的假设条件时,空间误差相关LM-Error渐近检验的水平扭曲较大,采用Bootstrap方法可以较好地降低该水平扭曲;不管模型误差是否满足独立正态分布的假设条件,Bootstrap方法均能够有效地降低LMError渐近检验的水平扭曲。     

空间自相关地理加权回归模型的估计

地理加权回归作为一类能有效处理回归分析中空间非平稳性现象的建模技术,在多类问题的研究得到了广泛的应用.主要讨论这类空间计量经济学模型在空间自相关情形下的估计问题.首先,对于因变量含有空间滞后项的地理加权回归模型,分别给出了局部似然估计和两步估计两种方法.其次,考虑了误差空间自相关下地理加权回归模型的估计问题.     

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     

回归模型的同方差检验

本文利用局部经验似然和WNW方法对条件分布函数和条件分位数进行估计,并利用条件分位数的方法对回归模型中的误差方差进行了同方差假设检验,获得了零假设下检验统计量的渐近分布为X2分布．模拟计算表明同方差假设检验的条件分位数方法具有较好的功效．     

Aligned rank tests in measurement error model

Aligned rank tests are introduced in the linear regression model with possible measurement errors. Unknown nuisance parameters are estimated first and then classical rank tests are applied on the residuals. Two situations are discussed: testing about an intercept in the linear regression model considering the slope parameter as nuisance and testing of parallelism of several regression lines, i.e. whether the slope parameters of all lines are equal. Theoretical results are derived and the simulation study is also made to illustrate good performance of introduced tests.     

Testing Lack-of-fit for a Polynomial Errors-in-variables Model

When a regression model is applied as an approximation of underlying model of data, the model checking is important and relevant. In this paper, we investigate the lack-of-fit test for a polynomial error-in-variables model. As the ordinary residuals are biased when there exist measurement errors in covariables,we correct them and then construct a residual-based test of score type. The constructed test is asymptotically chi-squared under null hypotheses. Simulation study shows that the test can maintain the significance level well.The choice of weight functions involved in the test statistic and the related power study are also investigated.The application to two examples is illustrated. The approach can be readily extended to handle more general models.     

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In this article, we develop efficient robust method for estimation of mean and covariance simultaneously for longitudinal data in regression model. Based on Cholesky decomposition for the covariance matrix and rewriting the regression model, we propose a weighted least square estimator, in which the weights are estimated under generalized empirical likelihood framework. The proposed estimator obtains high efficiency from the close connection to empirical likelihood method, and achieves robustness by bounding the weighted sum of squared residuals. Simulation study shows that, compared to existing robust estimation methods for longitudinal data, the proposed estimator has relatively high efficiency and comparable robustness. In the end, the proposed method is used to analyse a real data set.     

基于多目标规划法的模糊线性回归分析

讨论输入、输出均为模糊数,回归系数为实数时的模糊线性回归分析。由于模糊最小二乘线性回归容易受异常值的影响,而最小一乘法能有效地降低回归模型的误差。为此,基于最小一乘法,建立多目标规划模型并将其转化为非线性规划问题进行求解,从而实现模糊线性回归模型的参数估计。最后,结合一个数值实例,验证和比较该方法的合理性和优越性。     

"一带一路"与人文发展的空间依赖性分析

基于2014年"一带一路"沿线61个国家的人文发展指数,利用Moran'I空间自相关统计量检验"一带一路"沿线国家人文发展指数之间的空间自相关性,利用空间误差模型研究了"一带一路"战略对沿线国家的教育、医疗卫生等指数的影响.结果表明:"一带一路"沿线61国人文发展水平之间存在明显的空间自相关性,即空间聚集性和异质性并存;"一带一路"战略的实施必将对沿线国的教育、医疗卫生等发展做出积极贡献.     

Detecting and modeling nonlinearity in the gas furnace data

Using a modification of the Hinich, J Time Ser Anal 3(3):169–176, (1982) bispectrum test for nonlinearity and Gaussianity, the residuals of the Tiao and Box, J Am Stat Assoc 76:802–816, (1981) constrained and unconstrained VAR models for the gas furnace data reject the assumption of Gaussianity and linearity over a grid of bandwidths for estimating the bispectrum. These findings call into question the specification of the linear VAR and VARMA models assumed by Tiao and Box, J Am Stat Assoc 76:802–816, (1981). Utilizing the alternative Hinich J Nonparametr Stat 6:205–221, (1996) nonlinearity test, the residuals of the VAR model were shown to exhibit episodic nonlinearity. The sensitivity of the findings to outliers is investigated by estimating and testing the residuals of L1 and MINIMAX models from 1–6 lags. Building on the linear dynamic specification, a multivariate adaptive regression splines (MARS) model is estimated, using two software implementations, and shown to remove the nonlinearity in the residuals. Leverage plots were used to illustrate the “cost” of imposing a linearity assumption. Out-of-sample forecasting tests from 1–6 periods ahead found that using the sum-of-squared errors criteria, the MARS model out performed ACE, GAM and projection pursuit models.     

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In this paper, a vector parameter method for ridge regression is proposed. We choose the negative gradient of mean square error as vector direction and decide vector norm with the expectation constrains both of mean square error and of residual error. We come to conclusions that the mean square error is a decreasing function of vector norm while the residual error a increasing one. It is the monotonicity of the errors that leads to our expectation constrains. Since two conflict constrains are under consideration, our vector parameter ridge regression is expected to bear both satisfactory mean square error and acceptable residual error. Finally, a multi-collinearity model is given as an example.     

Statistical inference for multivariate longitudinal data with irregular auto-correlated error process

Multivariate longitudinal data arise frequently in a variety of applications, where multiple outcomes are measured repeatedly from the same subject. In this paper, we first propose a two-stage weighted least square estimation procedure for the regression coefficients when the random error follows an irregular autoregressive(AR) process, and establish asymptotic normality properties for the resulting estimators. We then apply the smoothly clipped absolute deviation(SCAD) variable selection approach to determine the order of the AR error process. We further propose a test statistic to check whether multiple responses are correlated at the same observation time, and derive the asymptotic distribution of the proposed test statistic. Several simulated examples and real data analysis are presented to illustrate the finite-sample performance of the proposed method.     

Model selection method based on maximal information coefficient of residuals

The traditional model selection criterions try to make a balance between fitted error and model complexity. Assumptions on the distribution of the response or the noise, which may be misspecified, should be made before using the traditional ones. In this article, we give a new model selection criterion, based on the assumption that noise term in the model is independent with explanatory variables, of minimizing the association strength between regression residuals and the response, with fewer assumptions. Maximal Information Coefficient (MIC), a recently proposed dependence measure, captures a wide range of associations, and gives almost the same score to different type of relationships with equal noise, so MIC is used to measure the association strength. Furthermore, partial maximal information coefficient (PMIC) is introduced to capture the association between two variables removing a third controlling random variable. In addition, the definition of general partial relationship is given.     

MODEL SELECTION METHOD BASED ON MAXIMAL INFORMATION COEFFICIENT OF RESIDUALS

The traditional model selection criterions try to make a balance between fitted error and model complexity. Assumptions on the distribution of the response or the noise, which may be misspecified, should be made before using the traditional ones. In this ar- ticle, we give a new model selection criterion, based on the assumption that noise term in the model is independent with explanatory variables, of minimizing the association strength between regression residuals and the response, with fewer assumptions. Maximal Information Coe~cient （MIC）, a recently proposed dependence measure, captures a wide range of associ- ations, and gives almost the same score to different type of relationships with equal noise, so MIC is used to measure the association strength. Furthermore, partial maximal information coefficient （PMIC） is introduced to capture the association between two variables removing a third controlling random variable. In addition, the definition of general partial relationship is given.     

On ecological aspects of dynamics for zero slope regression for water pollution in Chile

Zero slope regression is an important problem in chemometrics, ranging from challenges of intercept-bias and slope ‘corrections’ in spectrometry, up to analysis of administrative data on chemical pollution in water in the region of Arica and Parinacota. Such issue is really complex and it integrates problems of optimal design, symmetry of errors, stabilization of the variability of estimators, dynamical system for errors up to an administrative data challenges. In this article we introduce a realistic approach to zero slope regression problem from dynamical point of view. Linear regression is a widely used approach for data fitting under assumption of normally distributed residuals. Many times non-normal residuals are observed and also theoretically justified. Our solution to such problem uses the recently introduced inference function called score function of distribution. As a minimization criterion, the minimum information of residuals criterion is used. The score regression appears to be a direct generalization of the least-squares regression for an arbitrary known (believed) distribution of residuals. The score estimation is also distribution sensitive version of M-estimation. The capability of the method is demonstrated by water pollution data examples.     

Massively Parallel Nonparametric Regression,With an Application to Developmental Brain Mapping

A penalized approach is proposed for performing large numbers of parallel nonparametric analyses of either of two types: restricted likelihood ratio tests of a parametric regression model versus a general smooth alternative, and nonparametric regression. Compared with naïvely performing each analysis in turn, our techniques reduce computation time dramatically. Viewing the large collection of scatterplot smooths produced by our methods as functional data, we develop a clustering approach to summarize and visualize these results. Our approach is applicable to ultra-high-dimensional data, particularly data acquired by neuroimaging; we illustrate it with an analysis of developmental trajectories of functional connectivity at each of approximately 70,000 brain locations. Supplementary materials, including an appendix and an R package, are available online.     

Semiparametric Bayesian inference for mean-covariance regression models

In this paper, we propose a Bayesian semiparametric mean-covariance regression model with known covariance structures. A mixture model is used to describe the potential non-normal distribution of the regression errors. Moreover, an empirical likelihood adjusted mixture of Dirichlet process model is constructed to produce distributions with given mean and variance constraints. We illustrate through simulation studies that the proposed method provides better estimations in some non-normal cases. We also demonstrate the implementation of our method by analyzing the data set from a sleep deprivation study.     

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。     

Extreme value distribution of a recursive-type detector in a linear model

We study a CUSUM–type monitoring scheme designed to sequentially detect changes in the regression parameter of an underlying linear model. The test statistic used is based on recursive residuals. Main aim of this paper is to derive the limiting extreme value distribution under the null hypothesis of structural stability. The model assumptions are flexible enough to include rather general classes of error sequences such as augmented GARCH(1,1) processes. The result is underlined by an illustrative simulation study. Research partially supported by NSF grants DMS–0604670 and DMS–065242.