Iterative weighted partial spline least squares estimation in semiparametric modeling of longitudinal data

In this paper we consider the estimating problem of a semiparametric regression modelling whenthe data are longitudinal.An iterative weighted partial spline least squares estimator(IWPSLSE)for the para-metric component is proposed which is more efficient than the weighted partial spline least squares estimator(WPSLSE)with weights constructed by using the within-group partial spline least squares residuals in the sense     

Detection of outliers in weighted least squares regression

In multiple linear regression model, we have presupposed assumptions (independence, normality, variance homogeneity and so on) on error term. When case weights are given because of variance heterogeneity, we can estimate efficiently regression parameter using weighted least squares estimator. Unfortunately, this estimator is sensitive to outliers like ordinary least squares estimator. Thus, in this paper, we proposed some statistics for detection of outliers in weighted least squares regression.     

Robust Depth-Weighted Wavelet for Nonparametric Regression Models

In the nonparametric regression models, the original regression estimators including kernel estimator, Fourier series estimator and wavelet estimator are always constructed by the weighted sum of data, and the weights depend only on the distance between the design points and estimation points. As a result these estimators are not robust to the perturbations in data. In order to avoid this problem, a new nonparametric regression model, called the depth-weighted regression model, is introduced and then the depth-weighted wavelet estimation is defined. The new estimation is robust to the perturbations in data, which attains very high breakdown value close to 1/2. On the other hand, some asymptotic behaviours such as asymptotic normality are obtained. Some simulations illustrate that the proposed wavelet estimator is more robust than the original wavelet estimator and, as a price to pay for the robustness, the new method is slightly less efficient than the original method.     

Estimation of partially specified spatial panel data models with random-effects

In this article, we study estimation of a partially specified spatial panel data linear regression with random-effects. Under the conditions of exogenous spatial weighting matrix and exogenous regressors, we give an instrumental variable estimation. Under certain sufficient assumptions, we show that the proposed estimator for the finite dimensional parameter is root-N consistent and asymptotically normally distributed and the proposed estimator for the unknown function is consistent and asymptotically distributed. Consistent estimators for the asymptotic variance-covariance matrices of both the parametric and unknown components are provided. The Monte Carlo simulation results verify our theory and suggest that the approach has some practical value.     

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In this article, we develop efficient robust method for estimation of mean and covariance simultaneously for longitudinal data in regression model. Based on Cholesky decomposition for the covariance matrix and rewriting the regression model, we propose a weighted least square estimator, in which the weights are estimated under generalized empirical likelihood framework. The proposed estimator obtains high efficiency from the close connection to empirical likelihood method, and achieves robustness by bounding the weighted sum of squared residuals. Simulation study shows that, compared to existing robust estimation methods for longitudinal data, the proposed estimator has relatively high efficiency and comparable robustness. In the end, the proposed method is used to analyse a real data set.     

Minimum Disparity Estimation in Linear Regression Models: Distribution and Efficiency

This paper deals with the minimum disparity estimation in linear regression models. The estimators are defined as statistical quantities which minimize the blended weight Hellinger distance between a weighted kernel density estimator of errors and a smoothed model density of errors. It is shown that the estimators of the regression parameters are asymptotic normally distributed and efficient at the model if the weights of the density estimators are appropriately chosen.     

Asymptotic Normality of a Combined Regression Estimator

In this paper, we propose a combined regression estimator by using a parametric estimator and a nonparametric estimator of the regression function. The asymptotic distribution of this estimator is obtained for cases where the parametric regression model is correct, incorrect, and approximately correct. These distributional results imply that the combined estimator is superior to the kernel estimator in the sense that it can never do worse than the kernel estimator in terms of convergence rate and it has the same convergence rate as the parametric estimator in the case where the parametric model is correct. Unlike the parametric estimator, the combined estimator is robust to model misspecification. In addition, we also establish the asymptotic distribution of the estimator of the weight given to the parametric estimator in constructing the combined estimator. This can be used to construct consistent tests for the parametric regression model used to form the combined estimator.     

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.     

利用完全辅助信息的模型校正信息论方法 (英)

本文我们提出了使用调查数据中完全辅助信息的模型校正K-L相对熵最小化方法．在估计有限总体均值时我们的估计渐近等价于MC估计(Wu and Sitter(2001))．我们方法一个有吸引力的优点是,导出的权具有特征:pi>0和■pi=0 ．这使得可把此方法应用于估计分布函数和分位数．导出的分布函数估计量FMKL(y)渐近等价于广义回归估计,且本身是一分函数布．     

A robust and efficient adaptive reweighted estimator of multivariate location and scatter

This article proposes a reweighted estimator of multivariate location and scatter, with weights adaptively computed from the data. Its breakdown point and asymptotic behavior under elliptical distributions are established. This adaptive estimator is able to attain simultaneously the maximum possible breakdown point for affine equivariant estimators and full asymptotic efficiency at the multivariate normal distribution. For the special case of hard-rejection weights and the MCD as initial estimator, it is shown to be more efficient than its non-adaptive counterpart for a broad range of heavy-tailed elliptical distributions. A Monte Carlo study shows that the adaptive estimator is as robust as its non-adaptive relative for several types of bias-inducing contaminations, while it is remarkably more efficient under normality for sample sizes as small as 200.     

On Adaptive Combination of Regression Estimators

Consider the problem of choosing between two estimators of the regression function, where one estimator is based on stronger assumptions than the other and thus the rates of convergence are different. We propose a linear combination of the estimators where the weights are estimated by Mallows' C _L . The adaptive estimator retains the optimal rates of convergence and is an extension of Stein-type estimators considered by Li and Hwang (1984, Ann. Statist., 12, 887-897) and related to an estimator in Burman and Chaudhuri (1999, Ann. Inst. Statist. Math. (to appear)).     

Optimal prediction for linear regression with infinitely many parameters

The problem of optimal prediction in the stochastic linear regression model with infinitely many parameters is considered. We suggest a prediction method that outperforms asymptotically the ordinary least squares predictor. Moreover, if the random errors are Gaussian, the method is asymptotically minimax over ellipsoids in ?₂. The method is based on a regularized least squares estimator with weights of the Pinsker filter. We also consider the case of dynamic linear regression, which is important in the context of transfer function modeling.     

On efficient estimators of two seemingly unrelated regressions

In this paper, following the results presented in Liu’s work [Liu, A.Y., 2002. Efficient estimation of two seemingly unrelated regression equations. Journal of Multivariate Analysis 82, 445-456], we first represent the Gauss-Markov estimator of the regression parameter as a matrix series, and hence we conclude that the observation vectors should appear in any efficient estimator in pairs. Second, we prove that the simpler form of the two-stage Aitken estimator is unique. Finally we generalize our results to the system of two seemingly unrelated regressions with unequal numbers of observations and briefly summarize our conclusions.     

r-k Class estimation in regression model with concomitant variables

We treat with the r-k class estimation in a regression model, which includes the ordinary least squares estimator, the ordinary ridge regression estimator and the principal component regression estimator as special cases of the r-k class estimator. Many papers compared total mean square error of these estimators. Sarkar (1989, Ann. Inst. Statist. Math., 41, 717–724) asserts that the results of this comparison are still valid in a misspecified linear model. We point out some confusions of Sarkar and show additional conditions under which his assertion holds.     

Edgeworth expansion in censored linear regression model

For the censored simple linear regression model, we establish a oneterm Edgeworth expansion for the Koul, Susarla and Van Ryzin type estimator of the regression coefficient. Our approach is to represent the estimator of the regression coefficient as an asymptoticU-statistic plus some ignorable terms and hence apply the known results on the Edgeworth expansions for asymptoticU-statistic. The counting process and martingale techniques are used to provide the proof of the main results.     

Large and moderate deviations principles for kernel estimators of the multivariate regression

In this paper, we prove large deviations principle for the Nadaraya-Watson estimator and for the semi-recursive kernel estimator of the regression in the multidimensional case. Under suitable conditions, we show that the rate function is a good rate function. We thus generalize the results already obtained in the one-dimensional case for the Nadaraya-Watson estimator. Moreover, we give a moderate deviations principle for these two estimators. It turns out that the rate function obtained in the moderate deviations principle for the semi-recursive estimator is larger than the one obtained for the Nadaraya-Watson estimator.      

Convergence rate of the best-r-point-average estimator for the maximizer of a nonparametric regression function

The best-r-point-average (BRPA) estimator of the maximizer of a regression function, proposed in Changchien (in: M.T. Chao, P.E. Cheng (Eds.), Proceedings of the 1990 Taipei Symposium in Statistics, June 28–30, 1990, pp. 63–78) has certain merits over the estimators derived through the estimation of the regression function. Some of the properties of the BRPA estimator have been studied in Chen et al. (J. Multivariate Anal. 57 (1996) 191) and Bai and Huang (Sankhya: Indian J. Statist. Ser. A. 61 (Pt. 2) (1999) 208–217). In this article, we further study the properties of the BRPA estimator and give its convergence rate under some quite general conditions. Simulation results are presented for the illustration of the convergence rate. Some comparisons with existing estimators such as the Müller estimator are provided.     

Local asymptotic behavior of regression splines for marginal semiparametric models with longitudinal data

In this paper, we study the local asymptotic behavior of the regression spline estimator in the framework of marginal semiparametric model. Similarly to Zhu, Fung and He (2008), we give explicit expression for the asymptotic bias of regression spline estimator for nonparametric function f. Our results also show that the asymptotic bias of the regression spline estimator does not depend on the working covariance matrix, which distinguishes the regression splines from the smoothing splines and the seemingly u...     

Censored multiple regression by the method of average derivatives

This paper proposes a technique [termed censored average derivative estimation (CADE)] for studying estimation of the unknown regression function in nonparametric censored regression models with randomly censored samples. The CADE procedure involves three stages: firstly-transform the censored data into synthetic data or pseudo-responses using the inverse probability censoring weighted (IPCW) technique, secondly estimate the average derivatives of the regression function, and finally approximate the unknown regression function by an estimator of univariate regression using techniques for one-dimensional nonparametric censored regression. The CADE provides an easily implemented methodology for modelling the association between the response and a set of predictor variables when data are randomly censored. It also provides a technique for “dimension reduction” in nonparametric censored regression models. The average derivative estimator is shown to be root-n consistent and asymptotically normal. The estimator of the unknown regression function is a local linear kernel regression estimator and is shown to converge at the optimal one-dimensional nonparametric rate. Monte Carlo experiments show that the proposed estimators work quite well.     

简约SUR模型参数的协方差改进估计

考虑了SUR模型及其两个简约模型,给出简约模型下未知回归系数及其可估函数的协方差改进估计,并证明了在一定条件下该估计仍然是相应参数在原模型下的协方差改进估计.