Approximate conditional likelihood for generalized linear models with general missing data mechanism

The generalized linear model is an indispensable tool for analyzing non-Gaussian response data, with both canonical and non-canonical link functions comprehensively used. When missing values are present, many existing methods in the literature heavily depend on an unverifiable assumption of the missing data mechanism, and they fail when the assumption is violated. This paper proposes a missing data mechanism that is as generally applicable as possible, which includes both ignorable and nonignorable missing data cases, as well as both scenarios of missing values in response and covariate. Under this general missing data mechanism, the authors adopt an approximate conditional likelihood method to estimate unknown parameters. The authors rigorously establish the regularity conditions under which the unknown parameters are identifiable under the approximate conditional likelihood approach. For parameters that are identifiable, the authors prove the asymptotic normality of the estimators obtained by maximizing the approximate conditional likelihood. Some simulation studies are conducted to evaluate finite sample performance of the proposed estimators as well as estimators from some existing methods. Finally, the authors present a biomarker analysis in prostate cancer study to illustrate the proposed method.     

Efficient estimation of seemingly unrelated additive nonparametric regression models

This paper is concerned with the estimating problem of seemingly unrelated (SU) nonparametric additive regression models. A polynomial spline based two-stage efficient approach is proposed to estimate the nonparametric components, which takes both of the additive structure and correlation between equations into account. The asymptotic normality of the derived estimators are establishedi. The authors also show they own some advantages, including they are asymptotically more efficient than those based on only the individual regression equation and have an oracle property, which is the asymptotic distribution of each additive component is the same as it would be if the other components were known with certainty. Some simulation studies are conducted to illustrate the finite sample performance of the proposed procedure. Applying the proposed procedure to a real data set is also made.     

TWO-STAGE ESTIMATION FOR SEEMINGLY UNRELATED NONPARAMETRIC REGRESSION MODELS

This paper is concerned with the estimating problem of seemingly unrelated （SU） non- parametric regression models. The authors propose a new method to estimate the unknown functions, which is an extension of the two-stage procedure in the longitudinal data framework. The authors show the resulted estimators are asymptotically normal and more efficient than those based on only the individual regression equation. Some simulation studies are given in support of the asymptotic results. A real data from an ongoing environmental epidemiologie study are used to illustrate the proposed procedure.     

Comparison of Covariate Balance Weighting Methods in Estimating Treatment Effects

Different covariate balance weighting methods have been proposed by researchers from different perspectives to estimate the treatment effects. This paper gives a brief review of the covariate balancing propensity score method by Imai and Ratkovic (2014), the stable balance weighting procedure by Zubizarreta (2015), the calibration balance weighting approach by Chan, et al. (2016), and the integrated propensity score technique by Sant’Anna, et al. (2020). Simulations are conducted to illustrate the finite sample performance of both the average treatment effect and quantile treatment effect estimators based on different weighting methods. Simulation results show that in general, the covariate balance weighting methods can outperform the conventional maximum likelihood estimation method while the performance of the four covariate balance weighting methods varies with the data generating processes. Finally, the four covariate balance weighting methods are applied to estimate the treatment effects of the college graduate on personal annual income.

     

B-Spline Method for Spatio-Temporal Inverse Model

Inverse models can be used to estimate surface fluxes in terms of the observed atmospheric concentration measurement data. This paper proposes a new nonparametric spatio-temporal inverse model and provides the global expressions for the estimates by employing the B-spline method. The authors establish the asymptotic normality of the estimators under mild conditions. The authors also conduct numerical studies to evaluate the finite sample performance of the proposed methodologies. Finally, the authors apply the method to anthropogenic carbon dioxide (CO₂) emission data from different provinces of Canada to illustrate the validity of the proposed techniques.

     

Smooth estimation of ROC curve in the presence of auxiliary information

Receiver operating characteristic (ROC) curve is often used to study and compare two-sample problems in medicine. When more information may be available on one treatment than the other, one can improve estimator of ROC curve if the auxiliary population information is taken into account. The authors show that the empirical likelihood method can be naturally adapted to make efficient use of the auxiliary information to such problems. The authors propose a smoothed empirical likelihood estimator for ROC curve with some auxiliary information in medical studies. The proposed estimates are more efficient than those ROC estimators without any auxiliary information, in the sense of comparing asymptotic variances and mean squared error (MSE). Some asymptotic properties for the empirical likelihood estimation of ROC curve are established. A simulation study is presented to demonstrate the performance of the proposed estimators.     

The adaptive LASSO spline estimation of single-index model

In this paper, based on spline approximation, the authors propose a unified variable selection approach for single-index model via adaptive L ₁ penalty. The calculation methods of the proposed estimators are given on the basis of the known lars algorithm. Under some regular conditions, the authors demonstrate the asymptotic properties of the proposed estimators and the oracle properties of adaptive LASSO (aLASSO) variable selection. Simulations are used to investigate the performances of the proposed estimator and illustrate that it is effective for simultaneous variable selection as well as estimation of the single-index models.     

Robust estimation of parameters in nonlinear ordinary differential equation models

Ordinary differential equation (ODE) models are widely used to model dynamic processes in many scientific fields. Parameter estimation is usually a challenging problem, especially in nonlinear ODE models. The most popular method, nonlinear least square estimation, is shown to be strongly sensitive to outliers. In this paper, robust estimation of parameters using M-estimators is proposed, and their asymptotic properties are obtained under some regular conditions. The authors also provide a method to adjust Huber parameter automatically according to the observations. Moreover, a method is presented to estimate the initial values of parameters and state variables. The efficiency and robustness are well balanced in Huber estimators, which is demonstrated via numerical simulations and chlorides data analysis.     

Two-step estimators in partial linear models with missing response variables and error-prone covariates

A partial linear model with missing response variables and error-prone covariates is considered. The imputation approach is developed to estimate the regression coefficients and the nonparametric function. The proposed parametric estimators are shown to be asymptotically normal, and the estimators for the nonparametric part are proved to converge at an optimal rate. To construct confidence regions for the regression coefficients and the nonparametric function, respectively, the authors also propose the empirical-likelihood-based statistics and investigate the limit distributions of the empirical likelihood ratios. The simulation study is conducted to compare the finite sample behavior for the proposed estimators. An application to an AIDS dataset is illustrated.     

基于Copula的带截面相关二元选择面板模型估计研究

在很多情况下个体之间都会存在相关性,如果在利用极大似然估计时假设二元选择面板模型的扰动项是相互独立的, 那么模型参数的估计结果将不再是有效的.为此,通过将截面相关性纳入模型,构造了基于Copula函数的似然函数, 提出了一种两阶段极大似然估计,并证明了估计量的一致性和渐近正态性,以及方差的渐近形式.蒙特卡罗模拟表明新的估计方法明显改善了估计量的有效性.利用这个方法研究了国内上市公司现金分红行为的影响因素,发现销售增长率由不显著变得较为显著.     

Smoothed estimator of quantile residual lifetime for right censored data

It is of great interest to estimate quantile residual lifetime in medical science and many other ?elds. In survival analysis, Kaplan-Meier(K-M) estimator has been widely used to estimate the survival distribution. However, it is well-known that the K-M estimator is not continuous, thus it can not always be used to calculate quantile residual lifetime. In this paper, the authors propose a kernel smoothing method to give an estimator of quantile residual lifetime. By using modern empirical process techniques, the consistency and the asymptotic normality of the proposed estimator are provided neatly.The authors also present the empirical small sample performances of the estimator. De?ciency is introduced to compare the performance of the proposed estimator with the naive unsmoothed estimator of the quantile residaul lifetime. Further simulation studies indicate that the proposed estimator performs very well.     

Estimation of a subset of regression coefficients of interest in a model with non-spherical disturbances

This paper considers the estimation of a subset of regression coefficients in a linear regression model with non-spherical disturbances, when other regression coefficients are of no interest. A family of estimators is considered and its asymptotic distribution is derived. This proposed family of improved estimators is compared with the usual unrestricted FGLS estimator, and dominance conditions are obtained with respect to risk under quadratic loss as well as the Pitman nearness criterion. The results of a numerical simulation are presented to illustrate the risk performance of various estimators.     

The Asymptotic Properties of Scad Penalized Generalized Linear Models with Adaptive Designs

This paper discusses the asymptotic properties of the SCAD (smoothing clipped absolute deviation) penalized quasi-likelihood estimator for generalized linear models with adaptive designs, which extend the related results for independent observations to dependent observations. Under certain conditions, the authors proved that the SCAD penalized method correctly selects covariates with non-zero coefficients with probability converging to one, and the penalized quasi-likelihood estimators of non-zero coefficients have the same asymptotic distribution they would have if the zero coefficients were known in advance. That is, the SCAD estimator has consistency and oracle properties. At last, the results are illustrated by some simulations.

     

Robust Estimation for Partial Functional Linear Regression Model Based on Modal Regression

This paper presents a robust estimation procedure by using modal regression for the partial functional linear regression, which combines the common linear model with the functional linear regression model. The outstanding merit of the new method is that it is robust against outliers or heavy-tail error distributions while performs no worse than the least-square-based estimation method for normal error cases. The slope function is fitted by B-spline. Under suitable conditions, the authors obtain the convergence rates and asymptotic normality of the estimators. Finally, simulation studies and a real data example are conducted to examine the finite sample performance of the proposed method. Both the simulation results and the real data analysis confirm that the newly proposed method works very well.     

Single-Index Quantile Regression with Left Truncated Data

The purpose of this paper is two fold. First, the authors investigate quantile regression (QR) estimation for single-index QR models when the response is subject to random left truncation. The random weights are introduced to deal with left truncated data and the associated iteration estimation method is proposed. The asymptotic properties for the proposed QR estimates of the index parameter and unknown link function are both obtained. Further, by combining the QR loss function and the adaptive LASSO penalization, a variable selection procedure for the index parameter is introduced and its oracle property is established. Second, a weighted empirical log-likelihood ratio of the index parameter based on the QR method is introduced and is proved to be asymptotic standard chi-square distribution. Furthermore, confidence regions of the index parameter can be constructed. The finite sample performance of the proposed methods are demonstrated. A real data analysis is also conducted to show the usefulness of the proposed approaches.

     

自回归模型的加权复合Expectile回归估计及其应用

本文基于充分利用多个Expectile信息能提高参数估计效率的假设,提出了AR模型的加权复合Expectile回归(WCER)估计,探讨了该估计的最优权重,建立了其大样本性质,发现根据由数据驱动的最优权重所获得的WCER估计与最优权重已知时所获得的WCER估计具有相同的渐近有效性.数值模拟表明,当误差为厚尾或非对称分布,所提出的WCER估计大大优于传统最小二乘估计.即使误差分布未知,依然可以得到像极大似然估计一样具有优良统计性质的WCER估计.应用所提出的方法分析恒生指数和标准普尔500指数,实证分析表明:所提出的WCER估计在有效性意义下非常具有竞争力.     

基于OLS退势的单位根检验

研究了不同情形下OLS退势单位根检验统计量的性质.推导了检验统计量的渐近分布,同时,运用蒙特卡洛试验模拟了有限样本容量条件下检验统计量的分位数,在拟合分位数关于样本容量响应面函数的基础上,给出检验统计量不同样本容量条件下8个百分位数的估计值,为OLS退势单位根检验提供理论依据和检验用临界值表.     

Sequential empirical Bayesian design for sensitivity experiments

Maximum likelihood recursions were used by Wu (1985) to estimate extreme quantiles of a quantal response curve. For certain choices of initial designs, Wu’s method performs well. In many fields of application, there often exist some different initial designs which are known as the up-and-down designs. Based on the existing data set from such a design, the authors propose three sequential empirical Bayesian designs by quickly and efficiently exploiting the information in the testing data and known knowledge. The improvement obtained by using the new procedures for the estimation of extreme quantiles is substantial.     

Semiparametric analysis of isotonic errors-in-variables regression models with randomly right censored response

This paper considers the estimation of a semiparametric isotonic regression model when the covariates are measured with additive errors and the response is randomly right censored by a censoring time. The authors show that the proposed estimator of the regression parameter is rootn consistent and asymptotically normal. The authors also show that the isotonic estimator of the functional component, at a fixed point, is cubic root-n consistent and converges in distribution to the slope at zero of the greatest convex minorant of the sum of a two-sided standard Brownian motion and the square of the time parameter. A simulation study is carried out to investigate the performance of the estimators proposed in this article.     

线性回归模型的非线性稳健估计——基于经验过程理论的研究

线性回归模型参数估计的有效性及对厚尾扰动和离群值的稳健性有进一步改进的余地.本文基于条件分布函数提出线性参数模型的一种新的非线性稳健估计量,利用经验过程理论证明了其相合性和渐近正态性.相对于OLS(ordinary least squares)估计量和常用的稳健LAD(least absolute deviations)和Huber估计量,此估计量可全面把握因变量的分布信息,较准确地由样本数据反映真正的数据生成过程,关于扰动项的厚尾分布具有更好的稳健性,且可更好地消弱极端离群值样本对参数估计的不良影响.多种实验设计的模拟表明,此估计量在有限样本下表现良好;在厚尾扰动或离群值出现的时候,显示出良好的稳健性,且优于OLS、LAD以及Huber估计量的小样本表现.