Identification of LPV system using locally weighted technique

The problem of linear parameter varying （LPV） system identification is considered based on the locally weighted technique which provides estimation of the LPV model parameters at each distinct data time point by giving large weights to measurements that are ＂close＂ to the current time point and small weights to measurements ＂far＂ from the current time point. Issues such as choice of distance function, weighting function and bandwidth selection are discussed. The developed method is easy to implement and simulation results illustrate its efficiency.     

Functional-coefficient regression model and its estimation

Abstract. In this paper,a class of functional-coefficient regression models is proposed and an estimation procedure based on the locally weighted least equates is suggested. This class of models,with the proposed estimation method,is a powerful means for exploratory data analysis.     

基于地理加权回归的我国中东部城市商品房价格的空间特征分析

本文基于地理加权回归方法,分析了我国中东部地区主要大中城市商品房价格与人均工资和人口数之间回归关系的空间变化特征。结果表明,我国中东部地区主要大中城市的商品房价格除受地域位置的影响外,工资水平和人口数的影响强度在各地区也存在着显著差异,呈现显著的空间非平稳性。     

Nonparametric regression estimation in models with weak error's structure

In this paper we propose nonparametric estimates of the regression function and its derivative when it is only assumed a weak error's structure. We study their local and global asymptotic behaviour when we observe dependent trajectories.     

回归模型误差相关性的统一检验方法

提出了回归模型误差项关于实对称矩阵相关的概念，从而将探测误差项的各种相关性，诸如序列自相关、空间自相关以及趋势性等问题纳入统一的统计检验框架内．在线性回归模型下，提出了一种计算检验p-值的三阶矩χ^2逼近方法．与精确方法相比，该逼近方法不但显著地降低了计算量，而且模拟计算表明具有相当高的精度．     

半参数变系数部分线性模型的统计推断

本文在多种复杂数据下, 研究一类半参数变系数部分线性模型的统计推断理论和方法. 首先在纵向数据和测量误差数据等复杂数据下, 研究半参数变系数部分线性模型的经验似然推断问题, 分别提出分组的和纠偏的经验似然方法. 该方法可以有效地处理纵向数据的组内相关性给构造经验似然比函数所带来的困难. 其次在测量误差数据和缺失数据等复杂数据下, 研究模型的变量选择问题, 分别提出一个“纠偏” 的和基于借补值的变量选择方法. 该变量选择方法可以同时选择参数分量及非参数分量中的重要变量, 并且变量选择与回归系数的估计同时进行. 通过选择适当的惩罚参数, 证明该变量选择方法可以相合地识别出真实模型, 并且所得的正则估计具有oracle 性质.     

On resampling techniques for regression models

Resampling techniques like the bootstrap are examined for functions of the parameters of a linear model. A weighted resampling method analogous to the weighted jackknife developed by Hinkley (1977) is proposed for regression models.     

On statistical models for regression diagnostics

In regression diagnostics, the case deletion model (CDM) and the mean shift outlier model (MSOM) are commonly used in practice. In this paper we show that the estimates of CDM and MSOM are equal in a wide class of statistical models, which include LSE, MLE, Bayesian estimate andM-estimate in linear and nonlinear regression models; MLE in generalized linear models and exponential family nonlinear models; MLEs of transformation parameters of explanatory variables in a Box-Cox regression models and so on. Furthermore, we study some models, in which, the estimates are not exactly equal but are approximately equal for CDM and MSOM.     

Statistical inference using a weighted difference-based series approach for partially linear regression models

Partially linear regression models with fixed effects are useful tools for making econometric analyses and normalizing microarray data. Baltagi and Li (2002) [7] proposed a computation friendly difference-based series estimation (DSE) for them. We show that the DSE is not asymptotically efficient in most cases and further propose a weighted difference-based series estimation (WDSE). The weights in it do not involve any unknown parameters. The asymptotic properties of the resulting estimators are established for both balanced and unbalanced cases, and it is shown that they achieve a semiparametric efficient boundary. Additionally, we propose a variable selection procedure for identifying significant covariates in the parametric part of the semiparametric fixed-effects regression model. The method is based on a combination of the nonconcave penalization (Fan and Li, 2001 [13]) and weighted difference-based series estimation techniques. The resulting estimators have the oracle property; that is, they can correctly identify the true model as if the true model (the subset of variables with nonvanishing coefficients) were known in advance. Simulation studies are conducted and an application is given to demonstrate the finite sample performance of the proposed procedures.     

Efficient robust estimation of time-series regression models

The paper studies a new class of robust regression estimators based on the two-step least weighted squares (2S-LWS) estimator which employs data-adaptive weights determined from the empirical distribution or quantile functions of regression residuals obtained from an initial robust fit. Just like many existing two-step robust methods, the proposed 2S-LWS estimator preserves robust properties of the initial robust estimate. However, contrary to the existing methods, the first-order asymptotic behavior of 2S-LWS is fully independent of the initial estimate under mild conditions. We propose data-adaptive weighting schemes that perform well both in the cross-section and time-series data and prove the asymptotic normality and efficiency of the resulting procedure. A simulation study documents these theoretical properties in finite samples.     

Statistical estimation in varying coefficient models with surrogate data and validation sampling

Varying coefficient error-in-covariables models are considered with surrogate data and validation sampling. Without specifying any error structure equation, two estimators for the coefficient function vector are suggested by using the local linear kernel smoothing technique. The proposed estimators are proved to be asymptotically normal. A bootstrap procedure is suggested to estimate the asymptotic variances. The data-driven bandwidth selection method is discussed. A simulation study is conducted to evaluate the proposed estimating methods.     

Complete moment convergence for weighted sums of widely orthant-dependent random variables and its application in nonparametric regression models

We establish some results on the complete moment convergence for weighted sums of widely orthant-dependent (WOD) random variables, which improve and extend the corresponding results of Y. F. Wu, M. G. Zhai, and J. Y. Peng [J. Math. Inequal., 2019, 13(1): 251–260]. As an application of the main results, we investigate the complete consistency for the estimator in a nonparametric regression model based on WOD errors and provide some simulations to verify our theoretical results.     

On tests for selection of variables and independence under multivariate regression models

The authors consider various procedures for testing the hypotheses of independence of two sets of variables and certain regression coefficients are zero under multivariate regression model. Various properties of these procedures and the asymptotic distributions associated with these procedures are also considered.     

A semiparametric Wald statistic for testing logistic regression models based on case-control data

We propose a semiparametric Wald statistic to test the validity of logistic regression models based on case-control data. The test statistic is constructed using a semiparametric ROC curve estimator and a nonparametric ROC curve estimator. The statistic has an asymptotic chisquared distribution and is an alternative to the Kolmogorov-Smirnov-type statistic proposed by Qin and Zhang in 1997, the chi-squared-type statistic proposed by Zhang in 1999 and the information matrix test statistic proposed by Zhang in 2001. The statistic is easy to compute in the sense that it requires none of the following methods: using a bootstrap method to find its critical values, partitioning the sample data or inverting a high-dimensional matrix. We present some results on simulation and on analysis of two real examples. Moreover, we discuss how to extend our statistic to a family of statistics and how to construct its Kolmogorov-Smirnov counterpart. This work was supported by the 11.5 Natural Scientific Plan (Grant No. 2006BAD09A04) and Nanjing University Start Fund (Grant No. 020822410110)     

具有高斯过程误差的函数型线性模型的统计诊断

提出了具有高斯过程误差的函数型回归模型的几种诊断方法.在此模型中,首先,在样条基的基础上,推导了回归系数函数的估计.随后,证明了数据删失模型和均值漂移模型的等价性.然后,研究了三种诊断方法,即残差分析、Cook距离和似然距离来诊断异常和强影响数据.最后,通过一个模拟例子和一个实例来阐述方法的有效性.     

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.     

A variable selection method based on Tabu search for logistic regression models

A Tabu search method is proposed and analysed for selecting variables that are subsequently used in Logistic Regression Models. The aim is to find from among a set of m variables a smaller subset which enables the efficient classification of cases. Reducing dimensionality has some very well-known advantages that are summarized in literature. The specific problem consists in finding, for a small integer value of p, a subset of size p of the original set of variables that yields the greatest percentage of hits in Logistic Regression. The proposed Tabu search method performs a deep search in the solution space that alternates between a basic phase (that uses simple moves) and a diversification phase (to explore regions not previously visited). Testing shows that it obtains significantly better results than the Stepwise, Backward or Forward methods used by classic statistical packages. Some results of applying these methods are presented.     

Asymptotic behavior for bi-fractional regression models via Malliavin calculus

Let B^H1,K1 and BH2,K2 be two independent bi-fractional Brownian motions. In this paper, as a natural extension to the fractional regression model, we consider the asymptotic behavior of the sequence Sn：=∑i=0^n-1K（n^αBi^H,K1）（Bi＋1^H2,K2-Bi^H2,K2）where K is a standard Gaussian kernel function and the bandwidth parameter α satisfies certain hypotheses. We show that its limiting distribution is a mixed normal law involving the local time of the bi-fractional Brownian motion B^H1,K1. We also give the stable convergence of the sequence Sn by using the techniques of the Malliavin calculus.     

Properties of graphical regression models for multidimensional categorical data

We propose a two-component graphical chain model, the discrete regression distribution, where a set of discrete random variables is modeled as a response to a set of categorical and continuous covariates. The proposed model is useful for modeling a set of discrete variables measured at multiple sites along with a set of continuous and/or discrete covariates. The proposed model allows for joint examination of the dependence structure of the discrete response and observed covariates and also accommodates site-to-site variability. We develop the graphical model properties and theoretical justifications of this model. Our model has several advantages over the traditional logistic normal model used to analyze similar compositional data, including site-specific random effect terms and the incorporation of discrete and continuous covariates.