Mean estimation with data missing at random for functional covariables

In a missing-data setting, we want to estimate the mean of a scalar outcome, based on a sample in which an explanatory variable is observed for every subject while responses are missing by happenstance for some of them. We consider two kinds of estimates of the mean response when the explanatory variable is functional. One is based on the average of the predicted values and the second one is a functional adaptation of the Horvitz–Thompson estimator. We show that the infinite dimensionality of the problem does not affect the rates of convergence by stating that the estimates are root-n consistent, under missing at random (MAR) assumption. These asymptotic features are completed by simulated experiments illustrating the easiness of implementation and the good behaviour on finite sample sizes of the method. This is the first paper emphasizing that the insensitiveness of averaged estimates, well known in multivariate non-parametric statistics, remains true for an infinite-dimensional covariable. In this sense, this work opens the way for various other results of this kind in functional data analysis.     

Estimating a frequency distribution when the sampling is biased

A simple random sample on a random variable A allows its density to be consistently estimated, by a histogram or preferably a kernel density estimate. When the sampling is biased towards certain x-values these methods instead estimate a weighted version of the density function. This article proposes a method for estimating both the density and the sampling bias simultaneously. The technique requires two independent samples and utilises ideas from mark-recapture experiments. An estimator of the size of the sampled population also follows simply from this density estimate.     

Interdistributional Income Inequality

Incomplete moments are used to characterize income inequality and provide the basis for interdistributional Lorenz curves. Four measures of interdistributional inequality are considered and seen to be related to an interdistributional welfare interpretation. Based upon these measures, there has been a significant secular decline in interdistributional inequality between blacks and whites over the past 30 years.     

Estimation with right‐censored observations under a semi‐Markov model

The semi‐Markov process often provides a better framework than the classical Markov process for the analysis of events with multiple states. The purpose of this paper is twofold. First, we show that in the presence of right censoring, when the right end‐point of the support of the censoring time is strictly less than the right end‐point of the support of the semi‐Markov kernel, the transition probability of the semi‐Markov process is nonidentifiable, and the estimators proposed in the literature are inconsistent in general. We derive the set of all attainable values for the transition probability based on the censored data, and we propose a nonparametric inference procedure for the transition probability using this set. Second, the conventional approach to constructing confidence bands is not applicable for the semi‐Markov kernel and the sojourn time distribution. We propose new perturbation resampling methods to construct these confidence bands. Different weights and transformations are explored in the construction. We use simulation to examine our proposals and illustrate them with hospitalization data from a recent cancer survivor study. The Canadian Journal of Statistics 41: 237–256; 2013 © 2013 Statistical Society of Canada     

Nonparametric regression estimation in a null recurrent time series

We derive an asymptotic theory of nonparametric estimation for a time series regression model Z_t=f(X_t)+W_t, where {X_t} and {Z_t} are observed nonstationary processes, and {W_t} is an unobserved stationary process. The class of nonstationary processes allowed for {X_t} is a subclass of the class of null recurrent Markov chains. This subclass contains the random walk, unit root processes and nonlinear processes. The process {W_t} is assumed to be linear and stationary.     

支持MLS的多层次嵌入式高可信软件架构

为增强安全关键系统的高可信能力,在分析高可信保障机制现状的基础上,提出了一种多层次的高可信软件架构。该架构采用时空分离思想、虚拟机技术,为基于MLS的嵌入式安全关键系统提供了一种整体解决方案。基于该架构,研究了多层次的安全和防危策略管理方法、信息流控制机制、可信软件的评估和认证方法,为安全关键嵌入式系统提供可认证的安全服务。     

复杂系统质量生存决策的模型研究

在复杂经济系统的生存决策模型的基础上加入期望约束,提出并建立了一个基于资源、惯性和期望约束的质量生存决策的三维基本模型.由于决策系统的质量生存性由质量生存核维持,但在一般情况下得不到质量生存核的解析解,因此对其大小、形状、位置进行了理论分析,并根据理论分析结果,按照不同质量生存特性将三维决策空间进行了定性区域划分,最后用一个仿真实例进行了简单验证.     

“翻译腔”例析

因理解之误和表达之误所致,"翻译腔"表现各异.作者认为,在英汉翻译中,只有努力钻研原作,充分理解原文的深层含义,熟悉和掌握英汉语言的主要差异,表达符合译语语言习惯,才能使译文流畅自如,提高可接受性,消除"翻译腔".     

两度对话翻译教学模式的产生与阐释

笔者先将翻译流程设计在一个由原语形式到原型,再由原型到译语形式的折线之内,然后又将这一折线囊括在一个语境体系之中.其操作方式是"对话".其对话结果是通过语内和语际两度转换在语境体系的制约中实现的.     

Kernel estimation of a distribution function

A distribution function is estimated by a kernel method with

a poinrwise mean squared error criterion at a point x. Relation- ships between the mean squared error, the point x, the sample size and the required kernel smoothing parazeter are investigated for several distributions treated by Azzaiini (1981). In particular it is noted that at a centre of symmetry or near a mode of the distribution the kernei method breaks down. Point- wise estimation of a distribution function is motivated as a more useful technique than a reference range for preliminary medical diagnosis.