Efficient Estimation of a Distribution Function under Quadrant Dependence

LetX₁,X₂, ..., be real-valued random variables forming a strictly stationary sequence, and satisfying the basic requirement of being either pairwise positively quadrant dependent or pairwise negatively quadrant dependent. LetF^ be the marginal distribution function of theX_ips, which is estimated by the empirical distribution functionF_n and also by a smooth kernel-type estimateF_n, by means of the segmentX₁, ...,X_n. These estimates are compared on the basis of their mean squared errors (MSE). The main results of this paper are the following. Under certain regularity conditions, the optimal bandwidth (in the MSE sense) is determined, and is found to be the same as that in the independent identically distributed case. It is also shown thatn MSE(F_n(t)) andnMSE (F^_n(t)) tend to the same constant, asn→∞ so that one can not discriminate be tween the two estimates on the basis of the MSE. Next, ifi(n) = min {k∈{1, 2, ...}; MSE (F_k(t)) ≤ MSE (F_n(t))}, then it is proved thati(n)/n tends to 1, asn→∞. Thus, once again, one can not choose one estimate over the other in terms of their asymptotic relative efficiency. If, however, the squared bias ofF^_n(t) tends to 0 sufficiently fast, or equivalently, the bandwidthh_n satisfies the requirement thatnh³_n→ 0, asn→∞, it is shown that, for a suitable choice of the kernel, (i(n) ?n)/(nh_n) tends to a positive number, asn→∞ It follows that the deficiency ofF_n(t) with respect toF^_n(t),i(n) ?n, is substantial, and, actually, tends to ∞, asn→∞. In terms of deficiency, the smooth estimateF^_n(t) is preferable to the empirical distribution functionF_n(t)     

Estimation of critical points in the mixture inverse Gaussian model

The maximum likelihood estimation for the critical points of the failure rate and the mean residual life function are presented in the case of mixture inverse Gaussian model. Several important data sets are analyzed from this point of view. For each of the data sets, Bootstrapping is used to construct confidence intervals of the critical points.     

传说在西藏早期历史研究中的作用浅探

在西藏早期历史的研究中,传说的作用还没有引起广泛的重视。以传说为切点,通过藏汉文资料的对比分析,就会发现:传说不仅是文字产生之前历史的最重要载体,并且在文字产生后的很长一段时间里,仍对历史著述产生着重要的影响。对西藏早期史著中的传说和传说中的历史真实进行分析和辨别,无疑会对西藏早期历史的研究产生深远的影响。     

略论宗教在社会主义和谐社会建设中的积极作用

构建社会主义和谐社会是一项浩繁的事业,需要社会各界共同奋斗。宗教教义中蕴涵许多有关和谐的思想资源,我们应积极挖掘这些资源,采取多种方式和途径,动员信教群众努力为建设社会主义和谐社会做出贡献。     

A class of weighted dependence measures for bivariate failure time data

This paper considers a class of summary measures of the dependence between a pair of failure time variables over a finite follow-up region. The class consists of measures that are weighted averages of local dependence measures, and includes the cross-ratio-measure and finite region version of Kendall's τ; recently proposed by the authors. Two new special cases are identified that can avoid the need to estimate the bivariate survivor function and that admit explicit variance estimators. Nonparametric estimators of such dependence measures are proposed and are shown to be consistent and asymptotically normal with variances that can be consistently estimated. Properties of selected estimators are evaluated in a simulation study, and the method is illustrated through an analysis of Australian Twin Study data.     

Choice Functions: Rationality re-Examined

On analyzing the problem that arises whenever the set of maximal elements is large, and a selection is then required (see Peris & Subiza 1998), we realize that logical ways of selecting among maximals violate the classical notion and axioms of rationality. We arrive at the same conclusion if we analyze solutions to the problem of choosing from a tournament (where maximal elements do not necessarily exist). So, in our opinion the notion of rationality must be discussed, not only in the traditional sense of external conditions (Sen 1993), but in terms of the internal information provided by the binary relation.     

论当代中国政府经济职能的战略性重构

政府经济职能战略性重构的内涵是 :防止、纠补“政府失灵”和克服、弥补“市场失灵”。相应的对策 :一是限制和约束政府权力和职能 ,包括以政企分开为突破口 ,加快现代企业制度建设 ;规范政府干预职能及行为 ;加强对政府调控行为的监督 ;在政府经济职能重构的基础上 ,精简政府机构等。二是提升政府能力特别是宏观调控能力 ,包括财政宏观调控能力、金融宏观调控能力和行政组织调控能力 ;提高政府决策的科学化程度 ;将成本—效益观念和竞争机制引入政府调控的某些领域等 ,从而积极、适度、有效地行使政府对市场运作的宏观调控职能 ,充分发挥政府干预与市场调节二元机制的优势互补作用     

Characterizations based on conditional expectations

For given real functionsg andh, first we give necessary and sufficient conditions such that there exists a random variableX satisfying thatE(g(X)|X≥y)=h(y)r _x (y),∀y ∈ C _x , whereC _x andT _X are the support and the failure rate function ofX, respectively. These extend the results of Ruiz and Navarro (1994) and Ghitany et al. (1995). Next we investigate necessary and sufficient conditions such thath(y)=E(g(X)|X≥y), for a given functionh. Support for this research was provided in part by the National Science Council of the Republic of China, Grant No. NSC 86-2115-M-110-014 and NSC 88-2118-M-110-001     

M-quantile models with application to poverty mapping

Over the last decade there has been growing demand for estimates of population characteristics at small area level. Unfortunately, cost constraints in the design of sample surveys lead to small sample sizes within these areas and as a result direct estimation, using only the survey data, is inappropriate since it yields estimates with unacceptable levels of precision. Small area models are designed to tackle the small sample size problem. The most popular class of models for small area estimation is random effects models that include random area effects to account for between area variations. However, such models also depend on strong distributional assumptions, require a formal specification of the random part of the model and do not easily allow for outlier robust inference. An alternative approach to small area estimation that is based on the use of M-quantile models was recently proposed by Chambers and Tzavidis (Biometrika 93(2):255–268, 2006) and Tzavidis and Chambers (Robust prediction of small area means and distributions. Working paper, 2007). Unlike traditional random effects models, M-quantile models do not depend on strong distributional assumption and automatically provide outlier robust inference. In this paper we illustrate for the first time how M-quantile models can be practically employed for deriving small area estimates of poverty and inequality. The methodology we propose improves the traditional poverty mapping methods in the following ways: (a) it enables the estimation of the distribution function of the study variable within the small area of interest both under an M-quantile and a random effects model, (b) it provides analytical, instead of empirical, estimation of the mean squared error of the M-quantile small area mean estimates and (c) it employs a robust to outliers estimation method. The methodology is applied to data from the 2002 Living Standards Measurement Survey (LSMS) in Albania for estimating (a) district level estimates of the incidence of poverty in Albania, (b) district level inequality measures and (c) the distribution function of household per-capita consumption expenditure in each district. Small area estimates of poverty and inequality show that the poorest Albanian districts are in the mountainous regions (north and north east) with the wealthiest districts, which are also linked with high levels of inequality, in the coastal (south west) and southern part of country. We discuss the practical advantages of our methodology and note the consistency of our results with results from previous studies. We further demonstrate the usefulness of the M-quantile estimation framework through design-based simulations based on two realistic survey data sets containing small area information and show that the M-quantile approach may be preferable when the aim is to estimate the small area distribution function.     

个人教育收益率的估计与比较: 一个半参数方法

 本文运用一种变系数部分线性模型扩展了传统的明瑟人力资本收入函数,并提出了对明瑟函数中“平行性”假设的一种检验方法,以分析个人教育收益率如何受到工龄等因素的影响。通过对1991、2000以及2004等年度国家统计局城镇居民收入调查数据的分析,揭示出近二十年来我国城镇居民中不同工龄的人们的教育收益率存在明显区别,其中人教育收益率最高的始终是在1980年代中后期参加工作的群体。对导致我国教育收益率这种特殊现象的原因作了分析。