Test for Heteroscedasticity in Partially Linear Regression Models

Testing heteroscedasticity determines whether the regression model can predict the dependent variable consistently across all values of the explanatory variables. Since the proposed tests could not detect heteroscedasticity in all cases, more precisely in heavy-tailed distributions, the authors established new comprehensive test statistic based on Levene's test. The authors built the asymptotic normality of the test statistic under the null hypothesis of homoscedasticity based on the recent theory of analysis of variance for the infinite factors level. The proposed test uses the residuals from a regression model fit of the mean function with Levene's test to assess homogeneity of variance. Simulation studies show that our test yields better than other methods in almost all cases even if the variance is a nonlinear function. Finally, the proposed method is implemented through a real data-set.     

Robust Estimation for Partial Functional Linear Regression Model Based on Modal Regression

This paper presents a robust estimation procedure by using modal regression for the partial functional linear regression, which combines the common linear model with the functional linear regression model. The outstanding merit of the new method is that it is robust against outliers or heavy-tail error distributions while performs no worse than the least-square-based estimation method for normal error cases. The slope function is fitted by B-spline. Under suitable conditions, the authors obtain the convergence rates and asymptotic normality of the estimators. Finally, simulation studies and a real data example are conducted to examine the finite sample performance of the proposed method. Both the simulation results and the real data analysis confirm that the newly proposed method works very well.     

Empirical Likelihood Test for Regression Coefficients in High Dimensional Partially Linear Models

Journal of Systems Science and Complexity - This paper considers tests for regression coefficients in high dimensional partially linear Models. The authors first use the B-spline method to estimate...     

Estimation in Partially Observed Functional Linear Quantile Regression

Currently, working with partially observed functional data has attracted a greatly increasing attention, since there are many applications in which each functional curve may be observed only on a subset of a common domain, and the incompleteness makes most existing methods for functional data analysis ineffective. In this paper, motivated by the appealing characteristics of conditional quantile regression, the authors consider the functional linear quantile regression, assuming the explanatory f...     

多元线性回归模型的聚类分析方法研究

提出一种对大量的多元线性回归模型进行聚类分析的方法.首先利用增广矩阵的相关系数矩阵定义了2个多元回归模型之间的距离以及模型集合的质心和半径等相关概念.然后采用Squeezer聚类方法,以过程全自动化的方式,实现对多元线性回归模型集合进行聚类分析.通过仿真研究验证了方法的有效性,取得满意的分析结果.     

Diagnostics in Linear Regresion Model

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Partial Dynamic Dimension Reduction for Conditional Mean in Regression

Journal of Systems Science and Complexity - In many regression analysis, the authors are interested in regression mean of response variate given predictors, not its the conditional distribution....     

TWO-STAGE ESTIMATION FOR SEEMINGLY UNRELATED NONPARAMETRIC REGRESSION MODELS

This paper is concerned with the estimating problem of seemingly unrelated （SU） non- parametric regression models. The authors propose a new method to estimate the unknown functions, which is an extension of the two-stage procedure in the longitudinal data framework. The authors show the resulted estimators are asymptotically normal and more efficient than those based on only the individual regression equation. Some simulation studies are given in support of the asymptotic results. A real data from an ongoing environmental epidemiologie study are used to illustrate the proposed procedure.     

Partial Linear Model Averaging Prediction for Longitudinal Data

Prediction plays an important role in data analysis. Model averaging method generally provides better prediction than using any of its components. Even though model averaging has been extensively investigated under independent errors, few authors have considered model averaging for semiparametric models with correlated errors. In this paper, the authors offer an optimal model averaging method to improve the prediction in partially linear model for longitudinal data. The model averaging weights a...     

组合套期保值的多元线性回归特征

从统计学角度推导了风险头寸和多种套期保值工具所组成资产组合的价格协方差矩阵逆矩阵的表达式,分析了该表达式的统计学特征.在此基础上,结合组合套期保值策略的基本模型,研究了组合套期保值策略最优套期保值比率的数理统计特征.结果表明,各套期保值工具的最优套期保值比率正好等于风险头寸价格对各套期保值工具价格进行多元线性回归后对应的复回归系数.揭示了组合套期保值方法和套期保值的回归分析方法之间存在紧密的联系.     

Double Penalized Quantile Regression for the Linear Mixed Effects Model

Journal of Systems Science and Complexity - This paper proposes a double penalized quantile regression for linear mixed effects model, which can select fixed and random effects simultaneously....     

一元线性模型异方差的局部多项式回归

本文将局部多项式回归的非参数方法用于线性模型中异方差的估计 ,改进了传统的两阶段法 ,得到了估计的一致性和渐近正态性 ,为探讨估计的有限样本性 ,给出了若干模拟的例子。     

条件线性高斯状态空间模型的GSF-KF滤波算法

算法将模型中的条件线性状态方程代入观测方程,并融合线性状态的过程噪声和观测噪声,再与非线性状态方程联立,由高斯和滤波器(Gaussian sum filter,GSF)获得非线性状态的估计;然后将估计值代入线性状态方程与观测方程,由卡尔曼滤波器(Kalman Filter,KF)获得线性状态的估计.此外,获得的非线性状态估计的方差还用于修正线性状态的估计.将GSF-KF算法应用于目标跟踪的仿真结果表明,与现有Rao-Black-wellized粒子滤波器(Rao-Blackwellized ParticleFilter,RBPF)相比,新方法在保证精度的同时,明显提高了实时性,计算时间仅约为RBPF的7%.     

Least Squares Model Averaging for Two Non-Nested Linear Models

Journal of Systems Science and Complexity - This paper studies the least squares model averaging methods for two non-nested linear models. It is proved that the Mallows model averaging weight of...     

Empirical Likelihood for Generalized Linear Models with Longitudinal Data

Generalized linear models are usually adopted to model the discrete or nonnegative responses. In this paper, empirical likelihood inference for fixed design generalized linear models with longitudinal data is investigated. Under some mild conditions, the consistency and asymptotic normality of the maximum empirical likelihood estimator are established, and the asymptotic χ² distribution of the empirical log-likelihood ratio is also obtained. Compared with the existing results, the new...     

模糊线性回归及其应用实例

本文首先探讨了模糊线性回归模型的理论与方法,然后建立了天津市自来水行业职工人数预测模型,根据社会和经济发展目标,预测出天津自来水行业未来职工总人数。本文提出的方法与模型具有普遍意义与实用价值。     

Variable Selection of Varying Dispersion Student-t Regression Models

The Student-t regression model is a useful extension of the normal model,which can be used for statistical modeling of data sets involving errors with heavy tails and/or outliers and provides robust estimation of means and regression coefficients.In this paper,the varying dispersion Student-t regression model is discussed,in which both the mean and the dispersion depend upon explanatory variables.The problem of interest is simultaneously select significant variables both in mean and dispersion model.A unified procedure which can simultaneously select significant variable is given.With appropriate selection of the tuning parameters,the consistency and the oracle property of the regularized estimators are established.Both the simulation study and two real data examples are used to illustrate the proposed methodologies.     

Variable Selection via Generalized SELO-Penalized Cox Regression Models

The seamless-L_0(SELO) penalty is a smooth function that very closely resembles the L_0 penalty, which has been demonstrated theoretically and practically to be effective in nonconvex penalization for variable selection. In this paper, the authors first generalize the SELO penalty to a class of penalties retaining good features of SELO, and then develop variable selection and parameter estimation in Cox models using the proposed generalized SELO(GSELO) penalized log partial likelihood(PPL) approach. The authors show that the GSELO-PPL procedure possesses the oracle property with a diverging number of predictors under certain mild, interpretable regularity conditions. The entire path of GSELO-PPL estimates can be efficiently computed through a smoothing quasi-Newton(SQN) with continuation algorithm. The authors propose a consistent modified BIC(MBIC) tuning parameter selector for GSELO-PPL, and show that under some regularity conditions, the GSELOPPL-MBIC procedure consistently identifies the true model. Simulation studies and real data analysis are conducted to evaluate the finite sample performance of the proposed method.     

无失效指数分布参数的模糊加权最小二乘估计

无失效数据的出现，使分布参数的估计成为可靠性评定的又一关键问题。在对指数分布进行参数估计时，引入模糊加权系数，利用模糊加权最小二乘估计对数据进行回归拟合，推导出模糊加权失效率的估计式。由于无失效数据失效概率的确定对参数的估计结果有较大的影响，以减函数法确定失效概率的Bayes估计，并进行模糊加权线性回归。回归结果与常规线性回归结果相比，更接近工程实际。     

BP算法求解多元线性回归模型初探

提出求解多元线性回归模型系数的BP算法，给出该算法的数学描述、推导过程和计算机编程步骤，并结合实例说明。