Assessing the performance of the least developed countries in terms of the Millennium Development Goals

This article presents a proposal for assessing the progress of least developed countries towards the achievement of the Millennium Development Goals over the period 2000–2015. Composite indices are built to perform spatial and temporal benchmarking relying on the P2 Distance method. The results are contrasted with other indices developed under a multi-criterion approach with a double reference point. The main findings are that all the countries have improved their situation and country disparities have been reduced. Cambodia and Ethiopia have registered the best trends and South Sudan and Timor-Leste show the worse performance. Considering the position in the 2015 ranking, Rwanda and Bhutan performed the best, while Somalia and Chad rank in the last position. Having now reached the end of the Millennium Development Goals period, the gap with respect to the world average indicates that much work remains to be done in the 2030 Agenda for Sustainable Development.     

A GEOMETRIC CHARACTERIZATION OF LINEAR REGRESSION

This paper concerns the asymptotic properties of the maximum likelihood estimators of the parameters in a non regular Cox model involving a change-point in the regression on time-dependent covariates. The global consistency derives from the uniform convergence of the partial log-likelihood. We prove that the estimator of the change-point is n -consistent and the estimator of the regression parameter n 1/2 -consistent, and their asymptotic distributions are established.     

Rank statistics expressible as integrals under P–P-plots and receiver operating characteristic curves

Given a probability measure on the unit square, the measure of the region under an empirical P – P -plot defines a two-sample rank statistic. Instances include trimmed and censored versions of the Mann–Whitney–Wilcoxon statistic and a class of statistics with applications in the analysis of receiver operating characteristic (ROC) curves. A large sample distribution for such a statistic is obtained, which is valid under sampling from general populations. Explicit results are presented for comparing arbitrary quantile segments of two populations. The results are not restricted to continuous data and incorporate adjustments for tied values in the discrete case. A multivariate version of the large sample distribution extends the class of tractable statistics in ROC analysis and facilitates the use of methods based on partial areas when the data are discrete.     

Empirical assessment of the applicability of shrinkage predictors in regression when past and future data differ

Jones and Copas (1986) present theoretical and simulation results on the relative merits of a Stein predictor (Copas, 1983) and the ordinary least squares predictor in the usual linear multiple regression model, when certain distributional properties of the regressor variables arising in the past differ from those for which predictions are to be made. Here, extension is made to the practical situation where the true regression parameters are unknown. A hypothesis testing procedure is developed to help determine which of shrinkage and least squares is preferable in any given instance. This approach is applied to explain some empirical evidence on the comparative merits of the two procedures, recently given by Berk (1984).     

Einstein's First Published Paper

This article reviews Albert Einstein's first published paper, submitted for publication in 1900. At that time, Einstein was 21 and a recent college graduate. His paper uses modeling and least squares to analyze data in support of a scientific proposition. Einstein is shown to be well trained, for his day, in using statistics as a tool in his scientific research. This paper also shows his ability to make trivial arithmetic mistakes and some clumsiness in data recording. A major aim of this article is to help provide a better appreciation of Einstein as an active user of statistical arguments in this and other of his important publications.     

Permutation methods in relative risk regression models

In this paper, we develop a weighted permutation (WP) method to construct confidence intervals for regression parameters in relative risk regression models. The WP method is a generalized permutation approach. It constructs a resampled history which mimics the observed history for individuals under study. Inference procedures are based on studentized score statistics that are insensitive to the forms of the relative risk function. This makes the WP method appealing in the general framework of the relative risk regression model. First-order accuracy of the WP method is established using counting process approach with a partial likelihood filtration. A simulation study indicates that the method typically improves accuracy over asymptotic confidence intervals.     

Monte Carlo integration with Markov chain

There are two conceptually distinct tasks in Markov chain Monte Carlo (MCMC): a sampler is designed for simulating a Markov chain and then an estimator is constructed on the Markov chain for computing integrals and expectations. In this article, we aim to address the second task by extending the likelihood approach of Kong et al. for Monte Carlo integration. We consider a general Markov chain scheme and use partial likelihood for estimation. Basically, the Markov chain scheme is treated as a random design and a stratified estimator is defined for the baseline measure. Further, we propose useful techniques including subsampling, regulation, and amplification for achieving overall computational efficiency. Finally, we introduce approximate variance estimators for the point estimators. The method can yield substantially improved accuracy compared with Chib's estimator and the crude Monte Carlo estimator, as illustrated with three examples.     

A semiparametric Bayesian model for repeatedly repeated binary outcomes

Summary.  We discuss the analysis of data from single-nucleotide polymorphism arrays comparing tumour and normal tissues. The data consist of sequences of indicators for loss of heterozygosity (LOH) and involve three nested levels of repetition: chromosomes for a given patient, regions within chromosomes and single-nucleotide polymorphisms nested within regions. We propose to analyse these data by using a semiparametric model for multilevel repeated binary data. At the top level of the hierarchy we assume a sampling model for the observed binary LOH sequences that arises from a partial exchangeability argument. This implies a mixture of Markov chains model. The mixture is defined with respect to the Markov transition probabilities. We assume a non-parametric prior for the random-mixing measure. The resulting model takes the form of a semiparametric random-effects model with the matrix of transition probabilities being the random effects. The model includes appropriate dependence assumptions for the two remaining levels of the hierarchy, i.e. for regions within chromosomes and for chromosomes within patient. We use the model to identify regions of increased LOH in a data set coming from a study of treatment-related leukaemia in children with an initial cancer diagnostic. The model successfully identifies the desired regions and performs well compared with other available alternatives.     

广东省各地区市场化与经济增长关联度的经验研究

文章基于课题组所测得的广东省各地区2001年与2002年市场化指数的平行数据(Paneldata),运用最小中位数平方回归(theLeastMedianofSquaresregression,简称LMS)技术,对广东省各地区市场化与经济增长的关系进行了实证分析,充分考虑到了离群点(outliers)对于回归模型的影响,得出的结论是广东各地区市场化水平与经济发展水平及经济增长显著相关,短期市场化水平的变化与经济增长的关系不显著。