相依函数型数据的局部回归估计的渐近正态性

函数型数据研究近年来为越来越多的学者所重视,其在天文,医药,经济现象,生态环境及工业制造等诸多方面均有重要应用.非参数统计是统计研究的一个重要方面,其中核函数估计和局部多项式方法是这一类研究中重要常用方法.函数型数据的非参数方法中以核函数估计方法较为常见,且其收敛速度与极限分布无论在独立情形还是相依情形都有理论结果.而局部多项式的研究在函数型数据背景下较为少见,原因在于将局部多项式方法推广到函数型数据背景一直是一个难题. Marin, Ferraty, Vieu [Journal of Nonparametric Statistics, 22 (5) (2010), pp.617-632] 提出了非参函数型模型的局部回归估计. 这种估计可以看作是局部多项式估计在函数型数据背景下的一个推广.这种方法提出后,许多学者进一步研究了这种方法,考察了这种方法的收敛速度和极限分布,并将这种方法应用到不同的模型中以适应实际需求.但是,前人的研究都要求数据具有独立同分布的性质.然而许多实际数据并不符合这一假设.本文研究了在相依函数型数据情形下局部回归估计的渐近正态性.由于估计方法有差异,核函数估计的研究方法无法直接推广到局部回归估计,而相依性结构也给研究带来了一些挑战,我们采用Bernstein分块方法将相依性问题转化为渐近独立的问题,从而得到了估计的渐近正态性.此外我们还采用数据模拟的方法进一步验证了渐近正态的结果.     

Estimation of the inverse of mean

For the inverse of mean, a class of estimators with finite moments is considered and its properties are analyzed in the context of normal and non-normal populations.     

老年人与子女同住 对老年健康的影响分析

随着我国老龄化程度的持续加深和疾病谱的转变,当前社会存在大量老年照料需求,尽管国家和社会在积极构建养老服务体系,但短期内与子女同住的家庭养老模式仍将发挥重要作用。与子女同住会对老年健康产生一定的影响,这种影响对于不同健康程度的老年人也存在差异。本文基于南加州大学经济与社会研究中心提供的Harmonized CHARLS 2013-2015年追踪数据,选取我国60岁及以上老年群体为研究对象,以虚弱指数表征健康结果,采用OLS回归和分位数回归的方法探讨与子女同住的居住模式对老年健康的影响及这一影响对不同虚弱程度的老年人是否匀质,通过滞后模型设计和倾向值匹配法控制可能存在的内生性问题。研究发现居住模式与虚弱指数存在显著的正向关系,表明居住模式会影响老年健康水平;与子女同住对老年人健康存在负面效应,而在父母附近分而不离的居住模式相较于与子女同住而言对老年人的健康更为有利;与子女同住对老年健康的这种负向影响对于不同虚弱程度的老年人而言是非线性、非匀质的,大致呈先增后降的倒U形分布,表明不同健康状况的老年人对子女的照料需求是不同的,这种影响在不同性别、城乡和年龄段的老年群体间各有差异。这就为与子女同住的居住模式提供了一些警示,与子女同住不能改变老年健康衰减的趋势,应尽量减少或规避可能增加老年人晚年健康负担的风险性因素,让"家"真正成为老年人安享晚年的港湾。     

Analysis of Linear Models with One Factor Having Both Fixed and Random Levels

ABSTRACT

A general theory for a case where a factor has both fixed and random effect levels is developed under one-way treatment structure model. Estimation procedures for the fixed effects and variance components are consider for the model. The testing of fixed effects is considered when the variance–covariance matrix is known and unknown. Confidence intervals for estimable functions and prediction intervals for predictable functions are constructed. The computational procedures are illustrated using data from an on-farm trial.     

A Note on the Relation of Inverse-Probability-Weighting and Matching Estimators

This article compares the inverse-probability-of-selection-weighting estimation principle with the matching principle and derives conditions for weighting and matching to identify the same and the true distribution, respectively. This comparison improves the understanding of the relation of these estimation principles and allows constructing new estimators.     

Trace of the Variance-Covariance Matrix in Natural Exponential Families

In this article, we introduce the notion of trace variance function which is the trace of the variance-covariance matrix. Under some conditions, we prove that this trace variance function characterizes the Natural Exponential Family (NEF). We apply this characterization in order to estimate the distribution which belongs to some NEFs. Therefore, we introduce the estimator of this trace variance function. We give the asymptotic properties of this estimator. Finally, we illustrate our results using a simulation study.     

An extension of Franklin's randomized response technique for multi-proportions

ABSTRACT

In this article, we introduce six estimators, three based on row averages and the remaining three on column averages of population proportions for trichotomous population when randomized response sampling with a normal randomizing distribution is used. The estimators have been obtained using the method of moments. All the proposed estimators are shown to be unbiased and their variances have been worked out. The percent relative efficiencies of the column total based estimators with respect to row total based estimators are investigated through empirical study.     

Probability proportional to size (πps) sampling using ranks

There can be gains in estimation efficiency over equal probability samplin methods when one makes use of auxiliary information for probability proporti onal to size with replacement (πpswr) sampling methods. The usual method is simple to execute, but might lead to more than one appearance in the sampl e for any particular unit. When a suitable variable x is not available, one may know how to rank units reasonably well relative to the unknown y values before sample selection. When such ranking is possible, we introduce a simple and efficient sampling plan using the ranks as the unknown x measures of size. The proposed sampling plan is similar to, has the simplicity of, and has no greater sampling variance than with replacement sampling, but is without replacement.     

农民工参与就业培训的决定因素及对收入影响的实证分析

笔者利用在7个省市的调研数据,利用离散选择模型分析农民工参与就业培训的影响因素;同时,运用平均处理效应估计方法,考察参与就业培训对农民工收入水平的影响。分析结果说明,就业培训有助于提高农民工在就业市场的竞争力,提高农民工的收入水平。但这需要增加资金投入,加大宣传力度,正确引导营利性培训机构的发展。     

Evaluating the effect of education on earnings: models, methods and results from the National Child Development Survey

Summary.  Regression, matching, control function and instrumental variables methods for recovering the effect of education on individual earnings are reviewed for single treatments and sequential multiple treatments with and without heterogeneous returns. The sensitivity of the estimates once applied to a common data set is then explored. We show the importance of correcting for detailed test score and family background differences and of allowing for (observable) heterogeneity in returns. We find an average return of 27% for those completing higher education versus anything less. Compared with stopping at 16 years of age without qualifications, we find an average return to O-levels of 18%, to A-levels of 24% and to higher education of 48%.