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...     

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.     

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.     

Diagnostics in Linear Regresion Model

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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。     

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.     

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...     

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。     

复杂曲面拟合的相关向量机模型及其泛化能力

介绍相关向量机回归(RVM,Relevance Vector Machine)的基本原理。分析采用高斯径向基核函数时,核函数参数与模型性能之间的关系,并给出核函数参数选择建议。针对一个复杂非线性函数,采用均匀网格取样,并分别增加正态分布噪声和均匀分布噪声,分析RVM回归分析的拟合和泛化能力并与支持向量机(SVM,Support Vector Machine)回归模型作了比较。结果表明,SVM对样本数据的拟合能力优于RVM。但对于非训练样本,RVM的泛化能力要优于SVM,而且RVM模型更加稀疏,且在给出预测值的同时能够给出预测值的置信区间。     

成分数据的线性回归模型

在许多社会、经济、技术问题中，成分数据通常被用于研究作为整体的各部分的比率情况。本文结合对称的logratio变换与偏最小二乘回归方法，提出一种成分数据回归建模的方法。该方法可以克服经典线性回归方法在成分数据建模中的诸多困难。并反由于所采用的数学变换具有对称性，因此变换以后的变量可以较好地反映原始变量的含义，便于建立一个容易解释的数学模型。本文还采用北京市三次产业就业需求预测作为案例，说明成分数据回归建模的工作过程和应用价值，并通过计算结果验证了本文所提方法的有效性和合理性。     

Novel Criteria for Exponential Stability of Linear Non-Autonomous Functional Differential Equations

General linear non-autonomous functional differential equations are considered. Explicit criteria for exponential stability are given. Furthermore, the authors present an explicit robust stability bound for systems subject to time-varying perturbations. Two examples are given to illustrate the obtained results.     

区间数据下EV线性回归模型修正的广义最小二乘估计

研究了当响应变量为区间数据时的EV线性回归模型,通过构造区间数据的无偏转换,并对广义最小二乘估计作适当修正,得到了回归参数的估计,在较一般的条件下证明了强相合性和渐近正态性.最后作了若干模拟计算,从模拟的结果发现,利用本文提出的方法所获得的估计具有较高的精度.     

Sequential Estimate for Generalized Linear Models with Uncertain Number of Effective Variables

For the generalized linear model,the authors propose a sequential sampling procedure based on an adaptive shrinkage estimate of parameter.This method can determine a minimum sample size under which effective variables contributing to the model are identified and estimates of regression parameters achieve the required accuracy.The authors prove that the proposed sequential procedure is asymptotically optimal.Numerical simulation studies show that the proposed method can save a large number of samples compared to the traditional sequential approach.     

Sequential Feature Screening for Generalized Linear Models with Sparse Ultra-High Dimensional Data

This paper considers the iterative sequential lasso(ISLasso) variable selection for generalized linear model with ultrahigh dimensional feature space. The ISLasso selects features by estimated parameter sequentially iteratively for the second order approximation of likelihood function where the features selected depend on regulatory parameters. The procedure stops when extended BIC(EBIC)reaches a minimum. Simulation study demonstrates that the new method is a desirable approach over other methods.     

Estimation in Linear Regression with Laplace Measurement Error Using Tweedie-Type Formula

Based on a Tweedie-type formula developed under the Laplace distribution, this paper proposes a new bias-corrected estimator of the regression parameters in a simple linear model when the measurement error follows a Laplace distribution. Large sample properties, including the consistency and the asymptotic normality, are investigated. The finite sample performance of the proposed estimators are evaluated via simulation studies, as well as comparison studies with some existing estimation procedures.