纵向可加部分线性测量误差模型的渐近估计

基于纵向数据,研究参数部分协变量含有测量误差的可加部分线性测量误差模型的估计问题,提出了用于模型估计的偏差修正的二次推断函数方法,得到参数部分的估计结果具有相合性、渐近正态性,非参数可加函数的估计结果达到最优收敛速度。数值模拟和实例数据分析结果显示,该模型估计方法在同等条件下要优于广义估计方程方法。理论和数值结果显示,偏差修正的二次推断函数可以有效地处理测量误差和个体内相关性,是一个有效的纵向数据和测量误差数据分析工具,具有一定的理论和应用价值。     

纵向部分线性变系数EV模型的估计

纵向数据是随着时间变化对个体进行重复观测而得到的一种相关性数据，广泛出现在诸多科学研究领域。在对个体进行观测时，测量误差不可避免，忽略测量误差往往会导致有偏估计。本文利用二次推断函数方法研究关于纵向数据的参数部分和非参数部分协变量均含有测量误差的部分线性变系数测量误差(errors-in-variables, EV)模型的估计问题。利用B样条逼近模型中的未知系数函数，构造关于回归参数和B样条系数的偏差修正的二次推断函数以处理个体内相关性和测量误差，得到回归参数和变系数的偏差修正的二次推断函数估计，然后证明了估计方法和结果的渐近性质。数值模拟和实例数据分析结果显示本文提出的方法具有一定的实用价值。     

单调条件下部分线性回归模型的估计及渐进性质

探讨了部分线性回归模型当非参数分量受到单调条件限制时的估计问题,利用惩罚局部线性核估计方法给出参数分量与非参数分量αRLS、gRLS的估计,并进一步研究了^αRLS及^gRLS的渐进性质,结果表明:新得到的非参数约束条件下的估计是a.s.收敛的,并且保证了单调性和边界点适应性。将问题推广到一般情况,探讨了部分线性回归模型当非参数分量受到高阶导数约束时,参数分量的估计^αRLS。     

随机效应半参数logit模型的惩罚似然估计研究

 在颇具争议的收入差距和健康关系研究中,为了降低可能存在的模型设定和遗漏变量偏误,本文提出了随机效应半参数logit模型,其中非参数的设定还可用于数据的初探性分析。随后本文提出了模型非参数和参数部分的估计方法。这里涉及的难点是随机效应的存在导致似然函数中的积分没有解析式,而非参数的存在更加大了估计难度。本文基于惩罚样条非参数估计方法和四阶Laplace近似方法建立了惩罚对数似然函数,其最大化采用了Newton_Raphson近似方法。文章还建立了惩罚样条中重要光滑参数的选取准则。模型在收入差距和健康实例中的估计结果表明数据支持收入差距弱假说,且非参数估计结果表明其具有U型形式,与实例估计结果的比较指出本文提出的估计方法是较准确的。     

单指标纵向数据模型的估计

纵向数据是一类重要的相关性数据,广泛出现在诸多科研领域。单指标模型是多元非参数回归中重要的降维方法,在纵向数据下研究单指标模型是统计研究的热点问题。针对纵向数据单指标模型,提出惩罚改进二次推断函数方法来讨论模型的参数和非参数估计问题。该方法利用多项式样条回归方法逼近模型中的未知联系函数,将联系函数的估计转化为回归样条系数的估计,然后构造关于样条回归系数和单指标系数的惩罚改进二次推断函数,最小化惩罚改进二次推断函数便可得到模型的估计。理论结果显示,估计结果具有相合性和渐近正态性,最后得到了较好的数值模拟结果和实例数据分析结果,结果显示该方法适用于半参数纵向模型的参数和非参数估计问题。     

部分线性变系数模型的Backfitting约束估计

作为部分线性模型与变系数模型的推广,部分线性变系数模型是一类应用广泛的半参数模型.文章主要研究该模型线性部分存在约束条件下的估计和检验问题,首先基于backfitting方法给出了常数系数以及变系数部分的约束估计,其次构造了检验统计量用于检验约束条件.     

响应变量缺失下半参数变系数EV模型的约束统计推断

文章研究了半参数变系数EV模型在线性约束条件下的估计和检验问题,当响应变量缺失、非参数部分协变量带有测量误差时,利用局部纠偏的Profile最小二乘估计、Lagrange乘子方法和借补技术构造了回归模型参数分量两类纠偏约束估计量。此外,为了检验线性约束条件,构造了借补的Profile Lagrange乘子检验统计量,并通过蒙特卡洛数值模拟验证估计量和检验统计量的有效性。     

含缺失数据的半参数模型的稳健估计

文章在响应变量随机缺失下,基于分位数回归研究了半参数模型的稳健估计问题。首先基于B样条基函数近似技术,将模型非参数函数的估计问题转化为样条系数向量估计问题;其次,在响应变量随机缺失下,提出了一种新的插补方法,对缺失的响应变量进行多重插补;再次,基于插补后的数据集,构造出新的分位数目标函数,得到模型非参数函数以及参数向量的稳健估计;最后给出了有效算法计算多重插补估计量。通过模拟研究验证了所提方法的有效性和稳健性。     

函数系数协整模型局部线性估计方法的改进

函数系数协整模型可以克服非参数建模时的“维数困难”，同时体现系数的动态变化，被广泛应用于非平稳数据间复杂问题的研究。实践中经济序列常表现出时变波动方差和厚尾特征，传统核权最小二乘估计方法将不再适用。鉴于此，文章基于L1损失函数重构估计流程，选择表现稳健的局部线性核估计方法，并引入自适应方法，提出局部线性自适应最小绝对离差估计（ALADE）。模拟结果验证了所提估计方法可提升系数估计精度，优化模型整体拟合效果，同时绝对值交叉验证方法在选取最优窗宽时优势明显。实证分析发现，所提方法可识别中英两国汇率和价差间的动态协整关系，拟合系数平滑且接近理论值。     

TAR模型加权秩估计及其性质讨论

秩估计是上个世纪60年代逐渐兴起的一种非参数方法,由于它具有稳健性等特征,从而得到较为广泛的应用。本文主要讨论了TAR模型随机加权秩估计及其性质问题,证明了基于一般计分函数的线性秩统计量关于回归参数的渐近一致线性性。本文讨论的建立在计分规则基础上的秩估计方法,虽然以TAR模型为对象,但其基本原理同样可以应用到其他非线性模型的参数估计中。     

Polynomial Spline Estimation for a Generalized Additive Coefficient Model

Abstract.  We study a semiparametric generalized additive coefficient model (GACM), in which linear predictors in the conventional generalized linear models are generalized to unknown functions depending on certain covariates, and approximate the non-parametric functions by using polynomial spline. The asymptotic expansion with optimal rates of convergence for the estimators of the non-parametric part is established. Semiparametric generalized likelihood ratio test is also proposed to check if a non-parametric coefficient can be simplified as a parametric one. A conditional bootstrap version is suggested to approximate the distribution of the test under the null hypothesis. Extensive Monte Carlo simulation studies are conducted to examine the finite sample performance of the proposed methods. We further apply the proposed model and methods to a data set from a human visceral Leishmaniasis study conducted in Brazil from 1994 to 1997. Numerical results outperform the traditional generalized linear model and the proposed GACM is preferable.     

Empirical likelihood inference for parameters in a partially linear errors-in-variables model

In this paper, we consider the application of the empirical likelihood method to a partially linear model with measurement errors in the non-parametric part. It is shown that the empirical log-likelihood ratio at the true parameters converges to the standard chi-square distribution. Furthermore, we obtain the maximum empirical likelihood estimate of the unknown parameter by using the empirical log-likelihood ratio function, and the resulting estimator is shown to be asymptotically normal. Some simulations and an application are conducted to illustrate the proposed method.     

Nonparametric conditional mean imputation

Imputation is a much used method for handling missing data. It is appealing as it separates the missing data part of the analysis, which is handled by imputation, and the estimation part, which is handled by complete data methods. Most imputation methods, however, either rely on strict parametric assumptions or are rather ad hoc in which case they often only work approximately under even stricter assumptions. In this paper a non-parametric imputation method is proposed. Since it is non-parametric it works under quite general assumptions. In particular, a model for the complete data is not required in the imputation step, and the complete data method used after the imputation may be a general estimating equation for estimating a finite-dimensional parameter. Large sample results for the resulting estimator are given.     

Efficient Estimation in Marginal Partially Linear Models for Longitudinal/Clustered Data Using Splines

Abstract.  We consider marginal semiparametric partially linear models for longitudinal/clustered data and propose an estimation procedure based on a spline approximation of the non-parametric part of the model and an extension of the parametric marginal generalized estimating equations (GEE). Our estimates of both parametric part and non-parametric part of the model have properties parallel to those of parametric GEE, that is, the estimates are efficient if the covariance structure is correctly specified and they are still consistent and asymptotically normal even if the covariance structure is misspecified. By showing that our estimate achieves the semiparametric information bound, we actually establish the efficiency of estimating the parametric part of the model in a stronger sense than what is typically considered for GEE. The semiparametric efficiency of our estimate is obtained by assuming only conditional moment restrictions instead of the strict multivariate Gaussian error assumption.     

Inferences in dynamic logit models in semi-parametric setup for repeated binary data

Binary dynamic fixed and mixed logit models are extensively studied in the literature. These models are developed to examine the effects of certain fixed covariates through a parametric regression function as a part of the models. However, there are situations where one may like to consider more covariates in the model but their direct effect is not of interest. In this paper we propose a generalization of the existing binary dynamic logit (BDL) models to the semi-parametric longitudinal setup to address this issue of additional covariates. The regression function involved in such a semi-parametric BDL model contains (i) a parametric linear regression function in some primary covariates, and (ii) a non-parametric function in certain secondary covariates. We use a simple semi-parametric conditional quasi-likelihood approach for consistent estimation of the non-parametric function, and a semi-parametric likelihood approach for the joint estimation of the main regression and dynamic dependence parameters of the model. The finite sample performance of the estimation approaches is examined through a simulation study. The asymptotic properties of the estimators are also discussed. The proposed model and the estimation approaches are illustrated by reanalysing a longitudinal infectious disease data.     

Empirical likelihood inference in mixture of semiparametric varying-coefficient models for longitudinal data with non-ignorable dropout

In this paper, empirical likelihood inference in mixture of semiparametric varying-coefficient models for longitudinal data with non-ignorable dropout is investigated. We estimate the non-parametric function based on the estimating equations and the local linear profile-kernel method. An empirical log-likelihood ratio statistic for parametric components is proposed to construct confidence regions and is shown to be an asymptotically chi-squared distribution. The non-parametric version of Wilk's theorem is also derived. A simulation study is undertaken to illustrate the finite sample performance of the proposed method.     

An evaluation of a non-parametric method of estimating semi-variograms of isotropic spatial processes

Semi-variograms are useful for describing the correlation strucure of spatial random variables. Valid semi-variograms must be conditionally negative definite. To ensure this restriction when estimating these functions, a valid parametric model is typically fitted to a sample semi-variogram. Recently, a method of fitting valid semi-variograms without having to choose a parametric family has been described in the literature. The method is based on the spectral representation of positive definite functions. In this paper, the method is evaluated using simulated data. The fits obtained using the non-parametric method are compared with fits obtained by fitting four parametric models (exponential, Gaussian, rational quadratic and power) to simulated data using non-linear least squares. The comparisons are based on the integrated squared errors of the resulting fits. The non-parametric estimator always resulted in fits that were as good as those obtained using the parametric models. The non-parametric method is faster, easier to use and more objective than the parametric methods. Some examples are presented.     

A new information criterion-based bandwidth selection method for non-parametric regressions

ABSTRACT

Local linear estimator is a popularly used method to estimate the non-parametric regression functions, and many methods have been derived to estimate the smoothing parameter, or the bandwidth in this case. In this article, we propose an information criterion-based bandwidth selection method, with the degrees of freedom originally derived for non-parametric inferences. Unlike the plug-in method, the new method does not require preliminary parameters to be chosen in advance, and is computationally efficient compared to the cross-validation (CV) method. Numerical study shows that the new method performs better or comparable to existing plug-in method or CV method in terms of the estimation of the mean functions, and has lower variability than CV selectors. Real data applications are also provided to illustrate the effectiveness of the new method.     

Partially Linear Additive Models with Unknown Link Functions

In this paper, we consider partially linear additive models with an unknown link function, which include single‐index models and additive models as special cases. We use polynomial spline method for estimating the unknown link function as well as the component functions in the additive part. We establish that convergence rates for all nonparametric functions are the same as in one‐dimensional nonparametric regression. For a faster rate of the parametric part, we need to define appropriate ‘projection’ that is more complicated than that defined previously for partially linear additive models. Compared to previous approaches, a distinct advantage of our estimation approach in implementation is that estimation directly reduces estimation in the single‐index model and can thus deal with much larger dimensional problems than previous approaches for additive models with unknown link functions. Simulations and a real dataset are used to illustrate the proposed model.