删失数据下回归函数的加权局部复合分位数 回归估计

在右删失数据下,研究了误差具有异方差结构的非参数回归模型,利用局部多项式方法构造了回归函数的加权局部复合分位数回归估计,并得到了该估计的渐近正态性结果,最后通过模拟,当误差为重尾分布时,该估计比局部多项式估计以及核估计表现得更好.     

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.     

删失指标随机缺失下回归函数的复合分位数回归估计

在非参数回归模型中,传统的Nadaraya-Watson核估计和局部多项式估计常常因为误差为重尾情况而变得不稳健,Kai等人(2010)提出的复合分位数回归方法能弥补这一缺陷.文章在删失指标随机缺失的情况下,研究了误差具有异方差结构的非参数删失回归模型,利用局部多项式方法构造了回归函数的复合分位数回归估计,并得到了该估计的渐近正态性结果,把Kai等人(2010)的结果推广到删失指标随机缺失的右删失数据下.最后通过模拟发现,尤其是当误差为重尾分布时,该估计方法比Wang和Zheng (2014)提出的核估计方法更好.     

带有误差变量的自回归模型的局部多项式估计

该文主要研究带有误差变量的自回归模型的自回归函数的非参数估计问题,应用卷积核函数,给出了自回归函数的局部多项式估计,考察了局部多项式估计的相合性和渐近正态性,最后作了模拟计算.     

连续时间下非参数回归模型的误差密度估计

本文研究连续时间下非参数回归的误差密度估计问题，给出误差密度的一个核估计量，利用回归函数的核估计在紧区间上一致均收敛的结论证明了该统计量渐近无偏差，均方相合法，并说明了该核估计中窗宽选取的办法。     

NOD误差下非参数回归函数积分权估计的完全相合性

在误差为NOD序列的条件下,对Gassor和Müller提出的一类非参数回归函数积分权估计进行研究.利用截尾方法和NOD序列的指数不等式,得到了非参数回归函数积分权估计的完全相合性,结果推广和拓展了已有的相关结论.     

可加模型的无交叉分位回归曲线与房价问题研究

高维数据分析是当前研究的热点话题,而在对其进行分析时,非参数方法由于其灵活,无需对模型进行假定,得到了广泛的发展和认可。其中可加模型不仅能够有效地对变量进行降维,避免"维数灾难"的发生;而且能够得到各个变量的边际效应,具有很好的解释性。为了得到更加稳健的估计量,本文考虑利用分位回归方法对可加模型进行估计。分位回归方法由于其能够全面地刻画因变量在各个分位点上的变化趋势,并不受误差分布的限制,使得该方法具有更广泛的应用性。本文综合考虑以上优势,提出局部线性最小化检验函数估计方法和局部线性双核估计方法对可加模型进行估计。并且该方法能够有效地避免可加模型分位回归曲线的交叉问题.蒙特卡洛结果显示,与传统的均值估计法相比,不论误差分布的形式,我们提出的方法更具有优越性。用北京市二手房房价数据进行实证分析,进一步验证了本文提出的估计方法。     

非参数异方差回归模型的局部多项式估计——基于农村居民消费与收入的实证分析

本文主要研究非参数异方差回归模型的局部多项式估计问题.首先利用局部线性逼近的技巧,得到了回归均值函数的局部极大似然估计.然后,考虑到回归方差函数的非负性,利用局部对数多项式拟合,得到了方差函数的局部多项式估计,保证了估计量的非负性,并证明了估计量的渐近性质.最后,通过对农村居民消费与收入的实证研究,说明了非参数异方差回归模型的局部多项式方法比普通最小二乘估计法的拟合效果更好,并且预测的精度更高.     

固定设计下半参数回归模型核估计的渐近性质

研究一类新的半参数回归模型回归函数的核估计问题,其中误差项为一阶非参数自回归过程.通过重复利用Watson-Nadaraya核估计方法,构造了回归函数及误差回归函数的估计量分别为β,g(·)和ρ(·),在适当的条件下,证明了估计量β,g(·)和ρ(·)的渐近正态性.     

非线性自回归序列L1估计的渐近分布

由于时间序列数据中经常出现的厚尾特征使得通常的估计方法不再具有渐近的正态分布,在误差项二阶矩有限的条件下考虑了非线性自回归序列的L_1估计.采用局部线性近似的方法得到了具有凸样本路径的随机过程,在此基础上利用凸样本路径随机过程弱收敛的性质证明了非线性自回归序列L_1估计的渐近正态性及无偏性.     

A study over the general formula of regression sum of squares in multiple linear regression

In this study, in addition to the formula of regression sum of squares (SSR) in linear regression, a general formula of SSR in multiple linear regression is given. The derivations of the formula presented are given step by step. This new formula is proposed for estimation of the SSR in multiple linear regression. By using this formula, the researcher can find easily SSR and so the researcher can compose easily the table of variance analysis to interpret the regression made.     

Testing strict monotonicity in nonparametric regression

A new test for strict monotonicity of the regression function is proposed which is based on a composition of an estimate of the inverse of the regression function with a common regression estimate. This composition is equal to the identity if and only if the “true” regression function is strictly monotone, and a test based on an L ²-distance is investigated. The asymptotic normality of the corresponding test statistic is established under the null hypothesis of strict monotonicity.      

Sparse regression using mixed norms

Mixed norms are used to exploit in an easy way, both structure and sparsity in the framework of regression problems, and introduce implicitly couplings between regression coefficients. Regression is done through optimization problems, and corresponding algorithms are described and analyzed. Beside the classical sparse regression problem, multi-layered expansion on unions of dictionaries of signals are also considered. These sparse structured expansions are done subject to an exact reconstruction constraint, using a modified FOCUSS algorithm. When the mixed norms are used in the framework of regularized inverse problem, a thresholded Landweber iteration is used to minimize the corresponding variational problem.     

A bias corrected nonparametric regression estimator

In this article, we propose a new method of bias reduction in nonparametric regression estimation. The proposed new estimator has asymptotic bias order h⁴, where h is a smoothing parameter, in contrast to the usual bias order h² for the local linear regression. In addition, the proposed estimator has the same order of the asymptotic variance as the local linear regression. Our proposed method is closely related to the bias reduction method for kernel density estimation proposed by Chung and Lindsay (2011). However, our method is not a direct extension of their density estimate, but a totally new one based on the bias cancelation result of their proof.     

Rough support vector regression

This paper describes the relationship between support vector regression (SVR) and rough (or interval) patterns. SVR is the prediction component of the support vector techniques. Rough patterns are based on the notion of rough values, which consist of upper and lower bounds, and are used to effectively represent a range of variable values. Predictions of rough values in a variety of different forms within the context of interval algebra and fuzzy theory are attracting research interest. An extension of SVR, called rough support vector regression   (RSVR), is proposed to improve the modeling of rough patterns. In particular, it is argued that the upper and lower bounds should be modeled separately. The proposal is shown to be a more flexible version of lower possibilistic regression model using ?$?$-insensitivity. Experimental results on the Dow Jones Industrial Average demonstrate the suggested RSVR modeling technique.     

Adaptive local linear quantile regression

In this paper we propose a new method of local linear adaptive smoothing for nonparametric conditional quantile regression. Some theoretical properties of the procedure are investigated. Then we demonstrate the performance of the method on a simulated example and compare it with other methods. The simulation results demonstrate a reasonable performance of our method proposed especially in situations when the underlying image is piecewise linear or can be approximated by such images. Generally speaking, our method outperforms most other existing methods in the sense of the mean square estimation (MSE) and mean absolute estimation (MAE) criteria. The procedure is very stable with respect to increasing noise level and the algorithm can be easily applied to higher dimensional situations.     

Inequality constrained ridge regression estimator

We carry out the idea of inequality constrained least squares (ICLS) estimation of Liew (1976) to the inequality constrained ridge regression (ICRR) estimation. We propose ICRR estimator by reducing the primal–dual relation to the fundamental problem of Dantzig and Cottle, 1967, Cottle and Dantzig, 1974 with Lemke (1962) algorithm. Furthermore, we conduct a Monte Carlo experiment.     

在线Logistic回归

针对连续数据流分类问题,基于在线学习理论,提出一种在线logistic回归算法.研究带有正则项的在线logistic回归,提出了在线logistic-l2回归模型,并给出了理论界估计.最终实验结果表明,随着在线迭代次数的增加,提出的模型与算法能够达到离线预测的分类结果.本文工作为处理海量流数据分类问题提供了一种新的有效方法.