Variable selection for partially varying coefficient single-index model

In this paper, we consider the problem of variable selection for partially varying coefficient single-index model, and present a regularized variable selection procedure by combining basis function approximations with smoothly clipped absolute deviation penalty. The proposed procedure simultaneously selects significant variables in the single-index parametric components and the nonparametric coefficient function components. With appropriate selection of the tuning parameters, the consistency of the variable selection procedure and the oracle property of the estimators are established. Finite sample performance of the proposed method is illustrated by a simulation study and real data analysis.     

Combined-penalized likelihood estimations with a diverging number of parameters

In the economics and biological gene expression study area where a large number of variables will be involved, even when the predictors are independent, as long as the dimension is high, the maximum sample correlation can be large. Variable selection is a fundamental method to deal with such models. The ridge regression performs well when the predictors are highly correlated and some nonconcave penalized thresholding estimators enjoy the nice oracle property. In order to provide a satisfactory solution to the collinearity problem, in this paper we report the combined-penalization (CP) mixed by the nonconcave penalty and ridge, with a diverging number of parameters. It is observed that the CP estimator with a diverging number of parameters can correctly select covariates with nonzero coefficients and can estimate parameters simultaneously in the presence of multicollinearity. Simulation studies and a real data example demonstrate the well performance of the proposed method.     

Laplace Error Penalty‐based Variable Selection in High Dimension

We propose the Laplace Error Penalty (LEP) function for variable selection in high‐dimensional regression. Unlike penalty functions using piecewise splines construction, the LEP is constructed as an exponential function with two tuning parameters and is infinitely differentiable everywhere except at the origin. With this construction, the LEP‐based procedure acquires extra flexibility in variable selection, admits a unified derivative formula in optimization and is able to approximate the L₀ penalty as close as possible. We show that the LEP procedure can identify relevant predictors in exponentially high‐dimensional regression with normal errors. We also establish the oracle property for the LEP estimator. Although not being convex, the LEP yields a convex penalized least squares function under mild conditions if p is no greater than n. A coordinate descent majorization‐minimization algorithm is introduced to implement the LEP procedure. In simulations and a real data analysis, the LEP methodology performs favorably among competitive procedures.     

Empirical Likelihood for Censored Linear Regression and Variable Selection

The linear regression model for right censored data, also known as the accelerated failure time model using the logarithm of survival time as the response variable, is a useful alternative to the Cox proportional hazards model. Empirical likelihood as a non‐parametric approach has been demonstrated to have many desirable merits thanks to its robustness against model misspecification. However, the linear regression model with right censored data cannot directly benefit from the empirical likelihood for inferences mainly because of dependent elements in estimating equations of the conventional approach. In this paper, we propose an empirical likelihood approach with a new estimating equation for linear regression with right censored data. A nested coordinate algorithm with majorization is used for solving the optimization problems with non‐differentiable objective function. We show that the Wilks' theorem holds for the new empirical likelihood. We also consider the variable selection problem with empirical likelihood when the number of predictors can be large. Because the new estimating equation is non‐differentiable, a quadratic approximation is applied to study the asymptotic properties of penalized empirical likelihood. We prove the oracle properties and evaluate the properties with simulated data. We apply our method to a Surveillance, Epidemiology, and End Results small intestine cancer dataset.     

美学核心问题的再辨析与再审定

美是人与其世界在精神上相融为一的一体性状态.美只与人的神圣人性相关,但美学领域里却始终混杂着与人的动物性欲望相关的一系列内容,从而美学领域不仅混乱不堪,而且因为一系列非美学内容对真正美学内容的鹊巢鸠占而使美学处于有名无实的状态.因此,进一步辨析和审定美学的和非美学的具体内容,是美学存在下去并使它发挥实际作用的前提.     

Local Partitioned Regression

In this paper, we introduce a kernel‐based estimation principle for nonparametric models named local partitioned regression (LPR). This principle is a nonparametric generalization of the familiar partition regression in linear models. It has several key advantages: First, it generates estimators for a very large class of semi‐ and nonparametric models. A number of examples that are particularly relevant for economic applications will be discussed in this paper. This class contains the additive, partially linear, and varying coefficient models as well as several other models that have not been discussed in the literature. Second, LPR‐based estimators achieve optimality criteria: They have optimal speed of convergence and are oracle‐efficient. Moreover, they are simple in structure, widely applicable, and computationally inexpensive. A Monte Carlo simulation highlights these advantages.     

殷墟考古与商代甲骨文铜器铭文研究——纪念殷墟发掘80周年

80年来的殷墟考古,发掘出35000多片刻辞甲骨和有铭青铜器600多件,为商代甲骨和金文的研究提供了珍贵的资料。研究者将甲骨文晚商金文的有关资料与殷墟考古发现的遗迹、遗物相结合,研究商代社会（如商代的族氏、人物、官制）取得了重要成果。     

花园庄东地甲骨卜辞所见之动词同义词

通过对花园庄东地甲骨卜辞穷尽测查,共得动词同义词10组,本文对其中七组作了辨析。从中可以发现,卜辞中词所处的环境对于词义的确定有重要作用,卜辞同义词之间的差别更多的表现为语法功能和用法的不同,"进献"义同义词最为丰富,显示出当时的贡纳制度之盛。     

General composite quantile regression: Theory and methods

Abstract

In this article, we propose a new regression method called general composite quantile regression (GCQR) which releases the unrealistic finite error variance assumption being imposed by the traditional least squares (LS) method. Unlike the recently proposed composite quantile regression (CQR) method, our proposed GCQR allows any continuous non-uniform density/weight function. As a result, determination of the number of uniform quantile positions is not required. Most importantly, the proposed GCQR criterion can be readily transformed to a linear programing problem, which substantially reduces the computing time. Our theoretical and empirical results show that the GCQR is generally efficient than the CQR and LS if the weight function is appropriately chosen. The oracle properties of the penalized GCQR are also provided. Our simulation results are consistent with the derived theoretical findings. A real data example is analyzed to demonstrate our methodologies.