Root-n-consistent Estimation in Partial Linear Models with Long-memory Errors

We consider estimation of β in the semiparametric regression model y ( i ) - x ^T( i )β + f ( i / n ) + ε( i ) where x ( i ) = g ( i )/ n ) + e ( i , f and g are unknown smooth functions and the processes ε( i ) and e ( i ) are stationary with short- or long-range dependence. For the case of i.i.d. errors, Speckman (1988) proposed a √ n –consistent estimator of β. In this paper it is shown that, under suitable regularity conditions, this estimator is asymptotically unbiased and √ n –consistent even if the errors exhibit long-range dependence. The orders of the finite sample bias and of the required bandwidth depend on the long-memory parameters. Simulations and a data example illustrate the method     

An Improved Estimation in Regression Parameter Matrix in Multivariate Regression Model

We consider shrinkage and preliminary test estimation strategies for the matrix of regression parameters in multivariate multiple regression model in the presence of a natural linear constraint. We suggest a shrinkage and preliminary test estimation strategies for the parameter matrix. The goal of this article is to critically examine the relative performances of these estimators in the direction of the subspace and candidate subspace restricted type estimators. Our analytical and numerical results show that the proposed shrinkage and preliminary test estimators perform better than the benchmark estimator under candidate subspace and beyond. The methods are also applied on a real data set for illustrative purposes.     

基于GMM的缺失数据回归模型的半参数估计

响应变量存在数据缺失的情况广泛出现在社会经济研究中,对响应变量存在数据缺失的回归模型提出了一个在矩估计框架下的单一的半参数估计量,这种估计量保留了参数回归估计量与非参数匹配估计量的特性,从而使得该估计量既能在响应变量被观测的子样本中保持较好的拟合性,又能够降低响应变量未被观测的子样本的估计误差,并且证明了这种估计量是一致、渐进正态估计量。     

Estimation in the Cox cure model with covariates missing not at random,with application to disease screening/prediction

In an attempt to provide a statistical tool for disease screening and prediction, we propose a semiparametric approach to analysis of the Cox proportional hazards cure model in situations where the observations on the event time are subject to right censoring and some covariates are missing not at random. To facilitate the methodological development, we begin with semiparametric maximum likelihood estimation (SPMLE) assuming that the (conditional) distribution of the missing covariates is known. A variant of the EM algorithm is used to compute the estimator. We then adapt the SPMLE to a more practical situation where the distribution is unknown and there is a consistent estimator based on available information. We establish the consistency and weak convergence of the resulting pseudo-SPMLE, and identify a suitable variance estimator. The application of our inference procedure to disease screening and prediction is illustrated via empirical studies. The proposed approach is used to analyze the tuberculosis screening study data that motivated this research. Its finite-sample performance is examined by simulation.     

Estimation in semiparametric models using an auxiliary model

Two classes of semiparametric and nonparametric mixture models are defined to represent general kinds of prior information. For these models the nonparametric maximum likelihood estimator (NPMLE) of an unknown probability distribution is derived and is shown to be consistent and relative efficient. Linear functionals are used for the estimation of parameters. Their consistency is proved, the gain of efficiency is derived and asymptotical distributions are given.     

Parameter estimation for semiparametric ordinary differential equation models

Abstract

We propose a new class of two-stage parameter estimation methods for semiparametric ordinary differential equation (ODE) models. In the first stage, state variables are estimated using a penalized spline approach; In the second stage, form of numerical discretization algorithms for an ODE solver is used to formulate estimating equations. Estimated state variables from the first stage are used to obtain more data points for the second stage. Asymptotic properties for the proposed estimators are established. Simulation studies show that the method performs well, especially for small sample. Real life use of the method is illustrated using Influenza specific cell-trafficking study.     

Estimation of value-at-risk using single index quantile regression

ABSTRACT

Value-at-Risk (VaR) is one of the best known and most heavily used measures of financial risk. In this paper, we introduce a non-iterative semiparametric model for VaR estimation called the single index quantile regression time series (SIQRTS) model. To test its performance, we give an application to four major US market indices: the S&P 500 Index, the Russell 2000 Index, the Dow Jones Industrial Average, and the NASDAQ Composite Index. Our results suggest that this method has a good finite sample performance and often outperforms a number of commonly used methods.     

Ridge Regression for Estimation of Transition Probabilities from Aggregate Data

When data from several independent Markov chains are aggregated over each time point, least square estimation of transition probabilities faces the problem of multi-collinearity. We propose here an estimation procedure which involves use of ridge regression for the ordinary least square estimators. Performance of this estimator is then compared with that of the ordinary least squares.     

多辅助变量线性组合的回归估计

以提高估计量的精度为目的,定义了一种新的多个辅助变量的回归估计法,从理论上研究了该方法下权的选取方法,并将该方法下的估计量与Raj多辅助变量回归估计量、Ghosh多元线性回归估计量在精度上进行了数值比较,结果表明：这种新的多辅助变量的回归估计法在精度上优于Raj多辅助变量回归估计和Ghosh多元线性回归估计。     

Parameter Estimation in Conditional Heteroscedastic Models

Abstract

We study asymptotics of parameter estimates in conditional heteroscedastic models. The estimators considered are those obtained by minimizing certain functionals and those obtained by solving estimation equations. We establish consistency and derive asymptotic limit laws of the estimators. Condition under which the limit law is normal is studied. Further, bootstrap for these estimators is discussed. The limiting distribution of the estimators is not necessary always normal, and we present a real data example to illustrate this.     

正交多项式回归模型参数估计的格子设计及其最小二乘估计

对二元二次多项式回归模型进行预先正交化处理,提出使用因子空间的N等份的格子设计的观点,推导出了信息矩阵的一般性结构,并给出了该设计的非退化条件及其最小二乘估计和对应的协方差矩阵。     

Computational and statistical efficiency of semiparametric gls estimators

In this note, we report a dramatic improvement in the computational efficiency of semiparametric generalized least squares(SGLS) estimation. Computation of SGLS estimates no longer presents serious problems with data sets of moderate size. We also correct a numerical error in the standard errors of the SGLS estimates reported in our recent paper in this journal (Horowitz and Neumann, 1987). The corrected standard errors of SGLS are comparable to those we reported for quantile estimates.     

Semiparametric estimation of employment duration models

There are a variety of economic areas, such as studies of employment duration and of the durability of capital goods, in which data on important variables typically are censored. The standard techinques for estimating a model from censored data require the distributions of unobservable random components of the model to be specified a priori up to a finite set of parameters, and misspecification of these distributions usually leads to inconsistent parameter estimates. However, economic theory rarely gives guidance about distributions and the standard estimation techniques do not provide convenient methods for identifying distributions from censored data. Recently, several distribution-free or semiparametric methods for estimating censored regression models have been developed. This paper presents the results of using two such methods to estimate a model of employment duration. The paper reports the operating characteristics of the semiparametric estimators and compares the semiparametric estimates with those obtained from a standard parametric model.     

Computational and statistical efficiency of semiparametric gls estimators

In this note, we report a dramatic improvement in the computational efficiency of semiparametric generalized least squares(SGLS) estimation. Computation of SGLS estimates no longer presents serious problems with data sets of moderate size. We also correct a numerical error in the standard errors of the SGLS estimates reported in our recent paper in this journal (Horowitz and Neumann, 1987). The corrected standard errors of SGLS are comparable to those we reported for quantile estimates.     

On Variance Estimation in Semiparametric Regression Models

ABSTRACT

This article considers estimation of the error variance in a semiparametric regression model. The estimator, based on the semiparametric residuals, is shown to be consistent (with certain rate) for the error variance.     

About the Nonparametric Estimation of the Bernoulli Regression

The nonparametric estimation of the Bernoulli regression function is studied. The uniform consistency conditions are established and the limit theorems are proved for continuous functionals on C[a, 1 ? a], 0 < a < 1/2.     

空间回归模型估计中的最小二乘法

空间回归模型由于引入了空间地理信息而使得其参数估计变得复杂,因为主要采用最大似然法,致使一般人认为在空间回归模型参数估计中不存在最小二乘法。通过分析空间回归模型的参数估计技术,研究发现,最小二乘法和最大似然法分别用于估计空间回归模型的不同的参数,只有将两者结合起来才能快速有效地完成全部的参数估计。数理论证结果表明,空间回归模型参数最小二乘估计量是最佳线性无偏估计量。空间回归模型的回归参数可以在估计量为正态性的条件下而实施显著性检验,而空间效应参数则不可以用此方法进行检验。     

Parametrically Guided Non-parametric Regression

We present a new approach to regression function estimation in which a non-parametric regression estimator is guided by a parametric pilot estimate with the aim of reducing the bias. New classes of parametrically guided kernel weighted local polynomial estimators are introduced and formulae for asymptotic expectation and variance, hence approximated mean squared error and mean integrated squared error, are derived. It is shown that the new classes of estimators have the very same large sample variance as the estimators in the standard non-parametric setting, while there is substantial room for reducing the bias if the chosen parametric pilot function belongs to a wide neighbourhood around the true regression line. Bias reduction is discussed in light of examples and simulations.