An oracle property of the Nadaraya–Watson kernel estimator for high‐dimensional nonparametric regression

The Nadaraya–Watson estimator is among the most studied nonparametric regression methods. A classical result is that its convergence rate depends on the number of covariates and deteriorates quickly as the dimension grows. This underscores the “curse of dimensionality” and has limited its use in high‐dimensional settings. In this paper, however, we show that the Nadaraya–Watson estimator has an oracle property such that when the true regression function is single‐ or multi‐index, it discovers the low‐rank dependence structure between the response and the covariates, mitigating the curse of dimensionality. Specifically, we prove that, using K‐fold cross‐validation and a positive‐semidefinite bandwidth matrix, the Nadaraya–Watson estimator has a convergence rate that depends on the number of indices rather than on the number of covariates. This result follows by allowing the bandwidths to diverge to infinity rather than restricting them all to converge to zero at certain rates, as in previous theoretical studies.     

Averaging estimation for conditional covariance models

Estimating conditional covariance matrices is important in statistics and finance. In this paper, we propose an averaging estimator for the conditional covariance, which combines the estimates of marginal conditional covariance matrices by Model Averaging MArginal Regression of Li, Linton, and Lu. This estimator avoids the “curse of dimensionality” problem that the local constant estimator of Yin et al. suffered from. We establish the asymptotic properties of the averaging weights and that of the proposed conditional covariance estimator. The finite sample performances are augmented by simulation. An application to portfolio allocation illustrates the practical superiority of the averaging estimator.     

权利与宪法之思

权利是当今时代的主流话语,权利保障程度已经成为衡量一国法治发展水平的核心指标,宪法的产生及其发展亦是围绕保障公民权利这一话题而展开的。在此层面上,研究宪法与权利的关系就具有了重要的理论和实践意义。以此为切入点,主要可从形式上的差异与实质上的共生两大方面就权利与宪法的内在机理进行简要梳理：从时间、性质、运行以及规范层面剖析,权利与宪法之间的差异是形式上的;就其实质层面而言,两者又存在着紧密的共生关系。社会主义法治国家的建设应当紧紧围绕着权利与宪法这对核心范畴加以展开。     

Dimension reduced kernel estimation for distribution function with incomplete data

This work focuses on the estimation of distribution functions with incomplete data, where the variable of interest Y has ignorable missingness but the covariate X is always observed. When X is high dimensional, parametric approaches to incorporate X—information is encumbered by the risk of model misspecification and nonparametric approaches by the curse of dimensionality. We propose a semiparametric approach, which is developed under a nonparametric kernel regression framework, but with a parametric working index to condense the high dimensional X—information for reduced dimension. This kernel dimension reduction estimator has double robustness to model misspecification and is most efficient if the working index adequately conveys the X—information about the distribution of Y. Numerical studies indicate better performance of the semiparametric estimator over its parametric and nonparametric counterparts. We apply the kernel dimension reduction estimation to an HIV study for the effect of antiretroviral therapy on HIV virologic suppression.     

How to Make Model‐free Feature Screening Approaches for Full Data Applicable to the Case of Missing Response?

It is quite a challenge to develop model‐free feature screening approaches for missing response problems because the existing standard missing data analysis methods cannot be applied directly to high dimensional case. This paper develops some novel methods by borrowing information of missingness indicators such that any feature screening procedures for ultrahigh‐dimensional covariates with full data can be applied to missing response case. The first method is the so‐called missing indicator imputation screening, which is developed by proving that the set of the active predictors of interest for the response is a subset of the active predictors for the product of the response and missingness indicator under some mild conditions. As an alternative, another method called Venn diagram‐based approach is also developed. The sure screening property is proven for both methods. It is shown that the complete case analysis can also keep the sure screening property of any feature screening approach with sure screening property.     

Variable screening for ultrahigh dimensional censored quantile regression

Quantile regression is a flexible approach to assessing covariate effects on failure time, which has attracted considerable interest in survival analysis. When the dimension of covariates is much larger than the sample size, feature screening and variable selection become extremely important and indispensable. In this article, we introduce a new feature screening method for ultrahigh dimensional censored quantile regression. The proposed method can work for a general class of survival models, allow for heterogeneity of data and enjoy desirable properties including the sure screening property and the ranking consistency property. Moreover, an iterative version of screening algorithm has also been proposed to accommodate more complex situations. Monte Carlo simulation studies are designed to evaluate the finite sample performance under different model settings. We also illustrate the proposed methods through an empirical analysis.     

Principal varying coefficient estimator for high-dimensional models

ABSTRACT

We consider principal varying coefficient models in the high-dimensional setting, combined with variable selection, to reduce the effective number of parameters in semiparametric modelling. The estimation is based on B-splines approach. For the unpenalized estimator, we establish non-asymptotic bounds of the estimator and then establish the (asymptotic) local oracle property of the penalized estimator, as well as non-asymptotic error bounds. Monte Carlo studies reveal the favourable performance of the estimator and an application on a real dataset is presented.     

Objective Bayesian multiple comparisons for normal variances

This paper considers the multiple comparisons problem for normal variances. We propose a solution based on a Bayesian model selection procedure to this problem in which no subjective input is considered. We construct the intrinsic and fractional priors for which the Bayes factors and model selection probabilities are well defined. The posterior probability of each model is used as a model selection tool. The behaviour of these Bayes factors is compared with the Bayesian information criterion of Schwarz and some frequentist tests.     

HCIA--比较公司治理研究的新拓展

在一定意义上,企业制度是制度环境选择的结果.因此,比较公司治理研究应当引入比较制度分析,特别是历史比较制度分析的方法.     

论佛学影响六朝文学的三个维度

佛教作为六朝社会之重要文化类别,对其时之文学发展产生了广泛而深入的影响,而佛学对六朝文学之影响,主要存在三个维度:一曰语言维度,其影响包括佛经翻译提供新概念、佛经语言提供新风格、佛经唱读提供声韵新知识;二曰观念维度,其内容包括佛教一系列新观念影响文人的世界观、人生观和审美观;三曰思维维度,其影响内容包括佛学严密的逻辑性、中观思维方式、批驳辩难技巧等对文人创作思维的影响。