基尼加权回归分析：概念、方法及应用

普通最小二乘法是进行回归分析最常用的基本方法,但该方法要求满足若干经典假设,对于小样本或在与收入相关回归分析的参数估计中易受奇异值、高收入群体的影响。本文试图利用基尼加权回归弥补以上不足。基尼加权回归可分为参数方法与非参数方法两类,参数方法基于样本残差的基尼平均差最小原则对参数进行估计;非参数方法则是直接由两点间的斜率加权得到。基尼加权回归分析可以进行参数假设检验并定义拟合优度,其中的假设检验在实际应用中采用Jackknife重抽样方法估计方差。文中提出的样本拓展基尼平均差算法,弥补了现有算法对样本数据只能提供近似计算的不足,极大简化相应的计算公式。利用我国2015年省域截面数据、1994至2015年总量时间序列数据分别讨论入境旅游收入对收入基尼系数的影响,发现使用基尼加权回归的结果不仅符合理论预期,而且可以通过不平等厌恶参数的变化反映入境旅游收入对不同群体收入公平性的影响。     

Bounded-leverage weights for robust regression estimators

Both the least squares estimator and M-estimators of regression coefficients are susceptible to distortion when high leverage points occur among the predictor variables in a multiple linear regression model. In this article a weighting scheme which enables one to bound the leverage values of a weighted matrix of predictor variables is proposed. Bounded-leverage weighting of the predictor variables followed by M-estimation of the regression coefficients is shown to be effective in protecting against distortion due to extreme predictor-variable values, extreme response values, or outlier-induced multieollinearites. Bounded-leverage estimators can also protect against distortion by small groups of high leverage points.     

Weighted composite quantile regression for partially linear varying coefficient models

Partially linear varying coefficient models (PLVCMs) with heteroscedasticity are considered in this article. Based on composite quantile regression, we develop a weighted composite quantile regression (WCQR) to estimate the non parametric varying coefficient functions and the parametric regression coefficients. The WCQR is augmented using a data-driven weighting scheme. Moreover, the asymptotic normality of proposed estimators for both the parametric and non parametric parts are studied explicitly. In addition, by comparing the asymptotic relative efficiency theoretically and numerically, WCQR method all outperforms the CQR method and some other estimate methods. To achieve sparsity with high-dimensional covariates, we develop a variable selection procedure to select significant parametric components for the PLVCM and prove the method possessing the oracle property. Both simulations and data analysis are conducted to illustrate the finite-sample performance of the proposed methods.     

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

This article extends the spatial panel data regression with fixed-effects to the case where the regression function is partially linear and some regressors may be endogenous or predetermined. Under the assumption that the spatial weighting matrix is strictly exogenous, we propose a sieve two stage least squares (S2SLS) regression. Under some sufficient conditions, we show that the proposed estimator for the finite dimensional parameter is root-N consistent and asymptotically normally distributed and that the proposed estimator for the unknown function is consistent and also asymptotically normally distributed but at a rate slower than root-N. Consistent estimators for the asymptotic variances of the proposed estimators are provided. A small scale simulation study is conducted, and the simulation results show that the proposed procedure has good finite sample performance.     

Shrinkage Estimators of Intercept Parameters of Two Simple Regression Models with Suspected Equal Slopes

Estimators of the intercept parameter of a simple linear regression model involves the slope estimator. In this article, we consider the estimation of the intercept parameters of two linear regression models with normal errors, when it is a priori suspected that the two regression lines are parallel, but in doubt. We also introduce a coefficient of distrust as a measure of degree of lack of trust on the uncertain prior information regarding the equality of two slopes. Three different estimators of the intercept parameters are defined by using the sample data, the non sample uncertain prior information, an appropriate test statistic, and the coefficient of distrust. The relative performances of the unrestricted, shrinkage restricted and shrinkage preliminary test estimators are investigated based on the analyses of the bias and risk functions under quadratic loss. If the prior information is precise and the coefficient of distrust is small, the shrinkage preliminary test estimator overperforms the other estimators. An example based on a medical study is used to illustrate the method.     

Alternative GMM estimators for first-order autoregressive panel model: An improving efficiency approach

This article considers first-order autoregressive panel model that is a simple model for dynamic panel data (DPD) models. The generalized method of moments (GMM) gives efficient estimators for these models. This efficiency is affected by the choice of the weighting matrix that has been used in GMM estimation. The non-optimal weighting matrices have been used in the conventional GMM estimators. This led to a loss of efficiency. Therefore, we present new GMM estimators based on optimal or suboptimal weighting matrices. Monte Carlo study indicates that the bias and efficiency of the new estimators are more reliable than the conventional estimators.     

北京市城镇居民收入差距的定量分析

９０年代以来,北京市城镇居民收入有了很大提高,１９９０年人均生活费收入为１７８７．０８元,１９９７年为７８６１．７４元,扣除居民消费价格提高的影响,年平均增长速度为９．３％。但是,随着居民收入的普遍提高,居民之间收入差距也在逐渐扩大,这引起了社会的普遍关注,成为当前的经济热点问题之一。国际上通常用基尼系数来反映收入差距。根据表１和表２中北京市５００户城镇居民各类型人口构成和可支配收入构成资料,按万分法计算１９９６年和１９９７年基尼系数分别为０．１９１３和０．１９４０。通常认为,基尼系数小于０．２…     

On shrinkage least squares estimation in a parallelism problem

In a multi-sample simple regression model, generally, homogeneity of the regression slopes leads to improved estimation of the intercepts. Analogous to the preliminary test estimators, (smooth) shrinkage least squares estimators of Intercepts based on the James-Stein rule on regression slopes are considered. Relative pictures on the (asymptotic) risk of the classical, preliminary test and the shrinkage least squares estimators are also presented. None of the preliminary test and shrinkage least squares estimators may dominate over the other, though each of them fares well relative to the other estimators.     

收入波动与基尼系数:关于收入不平等的一个讨论

 本文建立了一个考察收入波动与基尼系数关系的模型,并通过计算机模拟实验证实：给定任何终生收入不平等状况,收入波动性增加都将导致各期的基尼系数增大。即,在终生收入不平等状况不变的情况下,各期的基尼系数也可因收入波动性增加而增大。考虑到我国经济转轨进程中家庭收入波动性日益增加的事实,则本文结论意味着,仅以基尼系数为判断标准很可能在一定程度上高估我国的家庭收入不平等状况。     

Minimum phi-divergence estimators for multinomial logistic regression with complex sample design

This article develops the theoretical framework needed to study the multinomial regression model for complex sample design with pseudo-minimum phi-divergence estimators. The numerical example and the simulation study propose new estimators for the parameter of the logistic regression with overdispersed multinomial distributions for the response variables, the pseudo-minimum Cressie–Read divergence estimators, as well as new estimators for the intra-cluster correlation coefficient. The simulation study shows that the Binder’s method for the intra-cluster correlation coefficient exhibits an excellent performance when the pseudo-minimum Cressie–Read divergence estimator, with \(\lambda =\frac{2}{3}\), is plugged.     

Handling missing data by deleting completely observed records

When data are missing, analyzing records that are completely observed may cause bias or inefficiency. Existing approaches in handling missing data include likelihood, imputation and inverse probability weighting. In this paper, we propose three estimators inspired by deleting some completely observed data in the regression setting. First, we generate artificial observation indicators that are independent of outcome given the observed data and draw inferences conditioning on the artificial observation indicators. Second, we propose a closely related weighting method. The proposed weighting method has more stable weights than those of the inverse probability weighting method (Zhao, L., Lipsitz, S., 1992. Designs and analysis of two-stage studies. Statistics in Medicine 11, 769–782). Third, we improve the efficiency of the proposed weighting estimator by subtracting the projection of the estimating function onto the nuisance tangent space. When data are missing completely at random, we show that the proposed estimators have asymptotic variances smaller than or equal to the variance of the estimator obtained from using completely observed records only. Asymptotic relative efficiency computation and simulation studies indicate that the proposed weighting estimators are more efficient than the inverse probability weighting estimators under wide range of practical situations especially when the missingness proportion is large.     

Inference about the Regression Parameters Using Median-Ranked Set Sampling

The ranked set samples and median ranked set samples in particular have been used extensively in the literature due to many reasons. In some situations, the experimenter may not be able to quantify or measure the response variable due to the high cost of data collection, however it may be easier to rank the subject of interest. The purpose of this article is to study the asymptotic distribution of the parameter estimators of the simple linear regression model. We show that these estimators using median ranked set sampling scheme converge in distribution to the normal distribution under weak conditions. Moreover, we derive large sample confidence intervals for the regression parameters as well as a large sample prediction interval for new observation. Also, we study the properties of these estimators for small sample setup and conduct a simulation study to investigate the behavior of the distributions of the proposed estimators.     

Kernel spline regression

The authors propose «kernel spline regression,» a method of combining spline regression and kernel smoothing by replacing the polynomial approximation for local polynomial kernel regression with the spline basis. The new approach retains the local weighting scheme and the use of a bandwidth to control the size of local neighborhood. The authors compute the bias and variance of the kernel linear spline estimator, which they compare with local linear regression. They show that kernel spline estimators can succeed in capturing the main features of the underlying curve more effectively than local polynomial regression when the curvature changes rapidly. They also show through simulation that kernel spline regression often performs better than ordinary spline regression and local polynomial regression.     

Preliminary test Liu-type estimators based on W,LR, and LM test statistics in a regression model

This article discusses the preliminary test approach for the regression parameter in multiple regression model. The preliminary test Liu-type estimators based on the Wald (W), Likelihood ratio (LR), and Lagrangian multiplier(LM) tests are presented, when it is supposed that the regression parameter may be restricted to a subspace. We also give the bias and mean squared error of the proposed estimators and the superior of the proposed estimators is also discussed.     

A note on the efficiency of composite quantile regression

Composite quantile regression (CQR) is motivated by the desire to have an estimator for linear regression models that avoids the breakdown of the least-squares estimator when the error variance is infinite, while having high relative efficiency even when the least-squares estimator is fully efficient. Here, we study two weighting schemes to further improve the efficiency of CQR, motivated by Jiang et al. [Oracle model selection for nonlinear models based on weighted composite quantile regression. Statist Sin. 2012;22:1479–1506]. In theory the two weighting schemes are asymptotically equivalent to each other and always result in more efficient estimators compared with CQR. Although the first weighting scheme is hard to implement, it sheds light on in what situations the improvement is expected to be large. A main contribution is to theoretically and empirically identify that standard CQR has good performance compared with weighted CQR only when the error density is logistic or close to logistic in shape, which was not noted in the literature.     

关于个人所得税公平效应的定量分析

成熟的个人所得税制度是其发挥公平效应的保障。通过定量分析发现，现行个人所得税免征额的每一次调整都会使高收入者比中低收入者受益更多，而超额累进税率结构设计不尽合理，对高收入者缺乏特殊税收政策，直接导致个人所得税难以发挥其调节收入差距和缓解贫富矛盾的公平效应。因此，应尽快改革税制，实行免征额指数化，减少税率级次，扩大低税率级距，对高收入者试行综合征收制，更好地发挥个人所得税的公平效应。     

Estimation in Varying-Coefficient Errors-in-Variables Models with Missing Response Variables

This article is concerned with the estimation of a varying-coefficient regression model when the response variable is sometimes missing and some of the covariates are measured with additive errors. We propose a class of estimators for the coefficient functions, as well as for the population mean and the error variance. The resulting estimators are shown to be asymptotically normal. Simulation studies are conducted to illustrate our approach.     

Difference-based estimation and model identification for panel data semiparametric models with cross-section dependence

Abstract

In this article, we consider a panel data partially linear regression model with fixed effect and non parametric time trend function. The data can be dependent cross individuals through linear regressor and error components. Unlike the methods using non parametric smoothing technique, a difference-based method is proposed to estimate linear regression coefficients of the model to avoid bandwidth selection. Here the difference technique is employed to eliminate the non parametric function effect, not the fixed effects, on linear regressor coefficient estimation totally. Therefore, a more efficient estimator for parametric part is anticipated, which is shown to be true by the simulation results. For the non parametric component, the polynomial spline technique is implemented. The asymptotic properties of estimators for parametric and non parametric parts are presented. We also show how to select informative ones from a number of covariates in the linear part by using smoothly clipped absolute deviation-penalized estimators on a difference-based least-squares objective function, and the resulting estimators perform asymptotically as well as the oracle procedure in terms of selecting the correct model.     

Unconditional Quantile Treatment Effects Under Endogeneity

This article develops estimators for unconditional quantile treatment effects when the treatment selection is endogenous. We use an instrumental variable (IV) to solve for the endogeneity of the binary treatment variable. Identification is based on a monotonicity assumption in the treatment choice equation and is achieved without any functional form restriction. We propose a weighting estimator that is extremely simple to implement. This estimator is root n consistent, asymptotically normally distributed, and its variance attains the semiparametric efficiency bound. We also show that including covariates in the estimation is not only necessary for consistency when the IV is itself confounded but also for efficiency when the instrument is valid unconditionally. An application of the suggested methods to the effects of fertility on the family income distribution illustrates their usefulness. Supplementary materials for this article are available online.     

Generalized Method of Moments Estimation When a Parameter Is on a Boundary

This article establishes the asymptotic distributions of generalized method of moments (GMM) estimators when the true parameter lies on the boundary of the parameter space. The conditions allow the estimator objective function to be nonsmooth and to depend on preliminary estimators. The boundary of the parameter space may be curved and/or kinked. The article discusses three examples: (1) instrumental variables (IV) estimation of a regression model with nonlinear equality and/or inequality restrictions on the parameters; (2) method of simulated moments estimation of a multinomial discrete response model with some random coefficient variances equal to 0, some random effect variances equal to 0, or some measurement error variances equal to 0; and (3) semiparametric least squares estimation of a partially linear regression model with nonlinear equality and/or inequality restrictions on the parameters.