On the correct regression function (in L2) and its applications when the dimension of the covariate vector is random

We derive the optimal regression function (i.e., the best approximation in the L₂ sense) when the vector of covariates has a random dimension. Furthermore, we consider applications of these results to problems in statistical regression and classification with missing covariates. It will be seen, perhaps surprisingly, that the correct regression function for the case with missing covariates can sometimes perform better than the usual regression function corresponding to the case with no missing covariates. This is because even if some of the covariates are missing, an indicator random variable δ$\delta$, which is always observable, and is equal to 1 if there are no missing values (and 0 otherwise), may have far more information and predictive power about the response variable Y than the missing covariates do. We also propose kernel-based procedures for estimating the correct regression function nonparametrically. As an alternative estimation procedure, we also consider the least-squares method.     

“Try to make it seem like we're regular kids”: Youth perceptions of restrictiveness in out-of-home care

While there are several measures of living environment restrictiveness, none has used the youth perspective in conceptualizing and operationalizing restrictiveness. The purpose of this qualitative study was to obtain the perspectives of child welfare involved youth who have lived in out-of-home care. Using focus group methodology, 40 youth were asked to define restriction and give examples of how it is operationalized in practice. Youth defined restriction as “rules”. The rules were about what youth can do, where they can go, who they can be with and how and with whom they can communicate. These rules were primarily characterized as inconsistent, arbitrary, non-individualized and developmentally inappropriate, although some characterized them as beneficial in the long term. Rules were mostly attributed to adult need for power and avoidance of legal responsibility for the youths. Typical feelings about the rules were anger, resentment, feeling labeled, isolated and stigmatized. Relationships influenced perceptions: within a positive relationship, youth understood and tolerated the rules that limited independence. The perception of what were normal restrictions for other youth not in out-of-home care was another influencing factor. These findings are examined in light of cognitive and affective development in adolescence. Recommendations for improving the measurement of living environment restrictiveness as well as enhancing child welfare services are proposed.     

Estimation of parameters in heavy-tailed distribution when its second order tail parameter is known

Estimating parameters in heavy-tailed distribution plays a central role in extreme value theory. It is well known that classical estimators based on the first order asymptotics such as the Hill, rank-based and QQ estimators are seriously biased under finer second order regular variation framework. To reduce the bias, many authors proposed the so-called second order reduced bias estimators for both first and second order tail parameters. In this work, estimation of parameters in heavy-tailed distributions are studied under the second order regular variation framework when the second order parameter in the distribution tail is known. This is motivated in large part by a recent work by the authors showing that the second order tail parameter is known for a large class of popular random difference equations (for example, ARCH models). The focus is on least squares estimators that generalize rank-based and QQ estimators. Though other possible estimators are also briefly discussed, the least squares estimators are most simple to use and perform best for finite samples in Monte Carlo simulations.     

外商直接投资影响因素的偏最小二乘回归建模分析

改革开放的20多年来,我国的外商直接投资逐年增加,对我国经济的快速发展发挥了重要的作用。而影响外商直接投资的因素有很多,不同的因素变量之间往往存在多重共线性或近似多重共线性关系,使得分析问题的难度加大。本文运用新型的多元统计数据分析方法——偏最小二乘(PLS)回归方法(既克服了传统方法的不足,又有效地消除了因素变量之间的多重共线性),分析了影响我国外商直接投资的因素,以及其影响程度,为我国进一步引进外商直接投资提供了有益的定量依据。     

zipf与省力原则

本文首先介绍Zipf的生平及以其名字命名的定律,然后讨论了省力原则与Zipf定律的关系:即,省力原则是单一化力量跟多样化力量之间的妥协,Zipf定律是省力原则的体现。并指出,省力原则与语言冗余现象不矛盾。在后半部分,我们讨论了省力原则与语用学的关系。Grice(1978)曾提出修订版奥卡姆剃刀(Occam’sRazor),这跟省力原则有明显的联系。Horn(1984)则进一步把Zipf的省力原则跟Grice的准则结合起来,提出了Q原则和R原则。Sperber和Wilson(1986/1995)的关联原则也谈到了省力问题,但他们的理论的解释力不如Horn的两原则大。最后,我们通过具体讨论如何理解anX,论证了我们的论点。     

动词隐含因果性和语篇话题性对回指选择的影响

动词隐含因果性和语篇话题性是制约回指选择的重要因素,但两者对回指选择的影响机制及交互作用仍不明确。语篇生成续写实验表明,动词隐含因果性确实会影响到后续指称对象的选择,并在原因类联结关系中得到加强;当动词语义倾向回指的对象为新引入的实体,而非语篇话题时,其回指倾向最显著。这说明基于给定语境生成语篇的过程遵循省力原则,但与语篇话题性相比,动词隐含因果性对回指倾向的制约更具刚性。     

异质性大数据的分布式估计

随着物联网技术的进步,大数据给网络带宽和计算机存储能力带来巨大挑战,传统的集中式数据处理难以实现,客观上促进了分布式统计学习的发展。在无迭代算法研究中,Zhang等(2013)证明了当数据集个数s=O(N) 时,基于局部经验风险最小化的分治(DC)简单平均估计量具有O(N-1)均方误差收敛速度,Huang和Huo(2019)在M估计框架下进一步提出分布式一步估计量,但上述方法均未考虑海量数据可能存在的异质性对分治估计效果的影响。本文在线性模型框架下提出海量异质数据的分治一步加权估计,证明了估计量的渐近性质并考虑了异质性检验问题。将本文提出的方法应用于美国医疗保险实际数据分析,结果表明该方法能更好地拟合数据的线性趋势且显著提高了计算效率。     

An Estimator of Shannon Entropy of Beta-Generated Distributions and a Goodness-of-Fit Test

The aim of this article is twofold: on the one hand to introduce and study some of the statistical properties of an estimator for the Shannon entropy and on the other hand to develop a goodness-of-fit test for beta-generated distributions and the distribution of order statistics. Beta-generated distributions are a broad class of univariate distributions which has received great attention during the last 15 years, as it obeys nice properties and it extends the distribution of order statistics. The proposed estimator of Shannon entropy of beta-generated distributions is motivated by the respective Vasicek’s estimator, as the latter one is tailored to the class of the beta-generated distributions and the distribution of order statistics. The estimator of Shannon entropy is defined and its consistency is studied. It is, moreover, exploited to build a goodness-of-fit test for the beta-generated distribution and the distribution of order statistics. Simulations are performed to examine the small- and moderate-sample properties of the proposed estimator and to compare the power of the proposed test with the power of competitors under a variety of alternatives.     

Prediction theory for autoregressivemoving average processes

This paper reviews statistical prediction theory for autoregressive-moving average processes wing techniques developed in control theory. It demonstrates explicitly the connectioluns between the statistical and control theory literatures. Both the forecasting problem and the Single extraction problem am considered, udng linear least squares methods. Whereas the classical Statistical theory developed by Wiener and Kolmogomv is restricted to stationary stochaotic processes, the recursive techniques known as the Kalman filter are shown to provide a satisfactory treatment of the difference-stationary care and other more general cases. Complete results for non-invertible moving averages are also obtained.