Bias-corrected estimators of scalar skew normal

One problem of skew normal model is the difficulty in estimating the shape parameter, for which the maximum likelihood estimate may be infinite when sample size is moderate. The existing estimators suffer from large bias even for moderate size samples. In this article, we proposed five estimators of the shape parameter for a scalar skew normal model, either by bias correction method or by solving a modified score equation. Simulation studies show that except bootstrap estimator, the proposed estimators have smaller bias compared to those estimators in literature for small and moderate samples.     

Data sharpening on unknown manifold

This article is concerned with data sharpening (DS) technique in nonparametric regression under the setting where the multivariate predictor is embedded in an unknown low-dimensional manifold. Theoretical asymptotic bias is derived, which reveals that the proposed DS estimator has a reduced bias compared to the usual local linear estimator. The asymptotic normality of the DS estimator is also developed. It can be confirmed from simulation and applications to real data that the bias reduction for the DS estimator supported on unknown manifold is evident.     

Local power of panel unit root tests allowing for structural breaks

The asymptotic local power of least squares–based fixed-T panel unit root tests allowing for a structural break in their individual effects and/or incidental trends of the AR(1) panel data model is studied. Limiting distributions of these tests are derived under a sequence of local alternatives, and analytic expressions show how their means and variances are functions of the break date and the time dimension of the panel. The considered tests have nontrivial local power in a N^?1/2 neighborhood of unity when the panel data model includes individual intercepts. For panel data models with incidental trends, the power of the tests becomes trivial in this neighborhood. However, this problem does not always appear if the tests allow for serial correlation in the error term and completely vanishes in the presence of cross-section correlation. These results show that fixed-T tests have very different theoretical properties than their large-T counterparts. Monte Carlo experiments demonstrate the usefulness of the asymptotic theory in small samples.     

Estimation bias and bias correction in reduced rank autoregressions

This paper characterizes the finite-sample bias of the maximum likelihood estimator (MLE) in a reduced rank vector autoregression and suggests two simulation-based bias corrections. One is a simple bootstrap implementation that approximates the bias at the MLE. The other is an iterative root-finding algorithm implemented using stochastic approximation methods. Both algorithms are shown to be improvements over the MLE, measured in terms of mean square error and mean absolute deviation. An illustration to US macroeconomic time series is given.     

Identifiability and bias reduction in the skew-probit model for a binary response

The skew-probit link function is one of the popular choices for modelling the success probability of a binary variable with regard to covariates. This link deviates from the probit link function in terms of a flexible skewness parameter. For this flexible link, the identifiability of the parameters is investigated. Next, to reduce the bias of the maximum likelihood estimator of the skew-probit model we propose to use the penalized likelihood approach. We consider three different penalty functions, and compare them via extensive simulation studies. Based on the simulation results we make some practical recommendations. For the illustration purpose, we analyse a real dataset on heart-disease.     

Local linear fitting and improved estimation near peaks

The authors look into the problem of estimating regression functions that exhibit jump irregularities in the first derivative. They investigate the behaviour of the bias in the local linear fit and show the superior performance of appropriate one‐sided versions of the local linear fit near such irregularities. They then propose an improved estimation procedure based on data‐driven selection of a conventional or one‐sided local linear fit according to a residual sum of squares type of criterion. The authors provide theoretical results and illustrate the method both on simulated and real‐life data examples. The Canadian Journal of Statistics 37: 453–475; 2009 © 2009 Statistical Society of Canada     

城市化视角下四川民族地区高校发展的瓶颈与对策

独特的自然地理环境、中国教育的传统功能及教育政策上的城市偏向三者交互作用形成了四川民族地区高校发展特有的发展瓶颈。破除四川民族地区高校发展瓶颈的根本出路在于加强院校之间合作与资源整合,开拓投资渠道与改善办学条件,对课程进行改革与重视校本课程开设,加强四川民族地区自身建设。     

资本技能互补与技术进步的技能偏向决定

本文基于三要素双层嵌套式CES生产函数和质量阶梯型技术创新模型，通过对企业行为的理论分析，揭示了决定技术进步方向的各种因素，发现技术进步的方向取决于技术进步的直接效应、资本技能互补的间接效应和劳动力市场内部的规模效应。其中，资本技能互补效应引致技术进步偏向于技能的机制有二：一是通过体现于资本的技术水平提高偏向于技能劳动，二是通过资本规模的扩大偏向于技能劳动。运用贝叶斯参数估计方法对中国1991-2016年期间技术进步技能偏向指数的实证测算结果表明，资本技能互补效应对于决定技术进步的技能偏向作用巨大，尽管在此期间直接效应偏向于非技能劳动，但是由于资本技能互补的间接效应和要素配置的规模效应偏向于技能劳动，且二者的作用强度均大于直接效应，从而使得中国的技术整体呈现出技能劳动偏向。     

Bias-Corrected maximum likelihood estimation of the parameters of the weighted Lindley distribution

The two-parameter weighted Lindley distribution is useful for modeling survival data, whereas its maximum likelihood estimators (MLEs) are biased in finite samples. This motivates us to construct nearly unbiased estimators for the unknown parameters. We adopt a “corrective” approach to derive modified MLEs that are bias-free to second order. We also consider an alternative bias-correction mechanism based on Efron’s bootstrap resampling. Monte Carlo simulations are conducted to compare the performance between the proposed and two previous methods in the literature. The numerical evidence shows that the bias-corrected estimators are extremely accurate even for very small sample sizes and are superior than the previous estimators in terms of biases and root mean squared errors. Finally, applications to two real datasets are presented for illustrative purposes.