Convergence assessment techniques for Markov chain Monte Carlo

MCMC methods have effectively revolutionised the field of Bayesian statistics over the past few years. Such methods provide invaluable tools to overcome problems with analytic intractability inherent in adopting the Bayesian approach to statistical modelling.However, any inference based upon MCMC output relies critically upon the assumption that the Markov chain being simulated has achieved a steady state or converged. Many techniques have been developed for trying to determine whether or not a particular Markov chain has converged, and this paper aims to review these methods with an emphasis on the mathematics underpinning these techniques, in an attempt to summarise the current state-of-play for convergence assessment techniques and to motivate directions for future research in this area.     

Quantitative central limit theorems for Mexican needlet coefficients on circular Poisson fields

The aim of this paper is to establish rates of convergence to Gaussianity for wavelet coefficients on circular Poisson random fields. This result is established by using the Stein–Malliavin techniques introduced by Peccati and Zheng (Electron J Probab 15(48):1487–1527, 2010) and the concentration properties of so-called Mexican needlets on the circle.     

Estimating the Optimum of a Stochastic System using Simulation

We incorporate new techniques for obtaining unbiased estimators of gradients from single simulations of stochastic systems in optimization procedures. We develop an "enhanced" least squares estimator of the optimum which incorporates information about both the function and its gradient and improves substantially on techniques which use only the function. We also propose a sequential design to use with the enhanced least squares estimator to optimize a regression function when it is evaluated by simulation.     

陕西高校各类教育提升全人素质的预测模型

采用"高校全人素质量表"随机抽样省部属8所高校4 953名大学生,对调查数据做SPSS多元回归参数估计和AMOS结构方程模型构建。结果表明,德育教育和专业教育分别对大学生全人素质16项指数产生显著正效应;德育教育"立德效应"主提升德道品质、心身健康、人生意义等素质;专业教育"树人效应"主提升求知钻研、学术探索、技术能力、语言思维等素质。研究结果为陕西高校全人素质教育提供了实证参数和理论依据。     

Parameter estimation in a highly non-linear model using simultaneous perturbation stochastic approximation

Often it is necessary to estimate the parameters of a model or unknown system. Various techniques exist to accomplish this task, including Kalman and Wiener filtering, least-mean-square (LMS) algorithms, and the Levenberg-Marquardt(L-M) algorithm. These techniques require an analytic form of the gradient of the function of the parameters to be estimated. A key feature of the simultaneous perturbation stochastic approximation (SPSA) method is that it is a gradient-free optimization technique (Spall; 1992,1998a,b, 1999). In the current problem, the function of parameters to be identified is highly non-linear and of sufficient difficulty that obtaining an analytic form of the gradient is impractical. Therefore, in this paper the

performance of the SPSA algorithm will be examined in terms of parameter selection, data requirements, and convergence performance on this non-linear problem. Results will be reported on both a first-order "standard" implementation of SPSA and on a second-order version of SPSA that tends to enhance convergence.     

Regression analysis of current-status data: an application to breast-feeding

"Although techniques for calculating mean survival time from current-status data are well known, their use in multiple regression models is somewhat troublesome. Using data on current breast-feeding behavior, this article considers a number of techniques that have been suggested in the literature, including parametric, nonparametric, and semiparametric models as well as the application of standard schedules. Models are tested in both proportional-odds and proportional-hazards frameworks....I fit [the] models to current status data on breast-feeding from the Demographic and Health Survey (DHS) in six countries: two African (Mali and Ondo State, Nigeria), two Asian (Indonesia and Sri Lanka), and two Latin American (Colombia and Peru)."     

Quasi-universal bandwidth selection for kernel density estimators

Let f?_n, h denote the kernel density estimate based on a sample of size n drawn from an unknown density f. Using techniques from L₂ projection density estimators, the author shows how to construct a data-driven estimator f?_n, h which satisfies This paper is inspired by work of Stone (1984), Devroye and Lugosi (1996) and Birge and Massart (1997).     

On the behaviour of some transforms of the sample correlation coefficient:discretebivariate populations

The present paper investigates for the first time, the robustness of some of the familiar transformations of the sample correlation coefficient when the parent population is discrete. Three specific cases examined are:The bivariate Poisson (BVP):the bivariate negative binomial (BNB):The trinomial (TN). Investigation of the (near) normality of the transformed statistics is done by the techniques considered by Subrahmaniam and Gajjar. In addition, an empirical examination of their behaviour is carried out by the density estimation technique due to Tarter and Kronmal.     

Measuring educational standards

Every summer, when English public examination results appear, there is a debate within the media about whether "educational standards" are changing. Harvey Goldstein argues that much of what passes for informed debate in the English media is both irrelevant and ill informed, and that there is no purely objective, statistical, means for measuring changes in "standards".     

Random Bernstein Polynomials

Random Bernstein polynomials which are also probability distribution functions on the closed unit interval are studied. The probability law of a Bernstein polynomial so defined provides a novel prior on the space of distribution functions on [0, 1] which has full support and can easily select absolutely continuous distribution functions with a continuous and smooth derivative. In particular, the Bernstein polynomial which approximates a Dirichlet process is studied. This may be of interest in Bayesian non-parametric inference. In the second part of the paper, we study the posterior from a "Bernstein–Dirichlet" prior and suggest a hybrid Monte Carlo approximation of it. The proposed algorithm has some aspects of novelty since the problem under examination has a "changing dimension" parameter space.     

Some extensions of anova techniques to location-scale models

In the usual analysis of variance (ANOVA) framework, the different distributions being compared are assumed to differ only in location so that the various measures of comparison are based on these location parameters only. The shift functions, introduced by Doksum (1974, provide a natural basis for extending some of the ANOVA techniques to nonlinear model so We consider a location-scale model and discuss several measures for comparing the various populations. These measures have intuitive interpretations in "control-treatments" situations. We develop various estimation procedures and discuss their large sample properties. Asymptotically efficient multiple comparison procedures are also considered.     

Simultaneous Confidence Bands and Hypothesis Testing in Varying-coefficient Models

Regression analysis is one of the most commonly used techniques in statistics. When the dimension of independent variables is high, it is difficult to conduct efficient non-parametric analysis straightforwardly from the data. As an important alternative to the additive and other non-parametric models, varying-coefficient models can reduce the modelling bias and avoid the "curse of dimensionality" significantly. In addition, the coefficient functions can easily be estimated via a simple local regression. Based on local polynomial techniques, we provide the asymptotic distribution for the maximum of the normalized deviations of the estimated coefficient functions away from the true coefficient functions. Using this result and the pre-asymptotic substitution idea for estimating biases and variances, simultaneous confidence bands for the underlying coefficient functions are constructed. An important question in the varying coefficient models is whether an estimated coefficient function is statistically significantly different from zero or a constant. Based on newly derived asymptotic theory, a formal procedure is proposed for testing whether a particular parametric form fits a given data set. Simulated and real-data examples are used to illustrate our techniques.     

On the $$L_p$$ norms of kernel regression estimators for incomplete data with applications to classification

We consider kernel methods to construct nonparametric estimators of a regression function based on incomplete data. To tackle the presence of incomplete covariates, we employ Horvitz–Thompson-type inverse weighting techniques, where the weights are the selection probabilities. The unknown selection probabilities are themselves estimated using (1) kernel regression, when the functional form of these probabilities are completely unknown, and (2) the least-squares method, when the selection probabilities belong to a known class of candidate functions. To assess the overall performance of the proposed estimators, we establish exponential upper bounds on the \(L_p\) norms, \(1\le p<\infty \), of our estimators; these bounds immediately yield various strong convergence results. We also apply our results to deal with the important problem of statistical classification with partially observed covariates.     

基于DEA模型评估江西省五市政府绩效实证研究

地区政府绩效评估自80年代以来日益受到重视,其评估指标体系不断完善,评估手段也日趋多元化。在以往的地方政府绩效相对有效性的评估中,往往很难兼顾评估的综合性和客观性。鉴于此,文章尝试应用DEA模型,在2004年8月国家人事部《中国地方政府绩效评估》课题组提出的33评估体系的基础上,选用代表性指标,对江西省人均GDP位居前五位的南昌、九江等五个市的政府绩效进行评估,得出一些结论并提供若干政策建议,从而进一步说明DEA模型评估政府绩效的有效性及适用范围。     

A bayesian predictive approach to the selection of variables in multiple regression

The squared error loss function applied to Bayesian predictive distributions is investigated as a variable selection criterion in linear regression equations. It is illustrated that “cost-free” variables may be eliminated if they are poor predictors. Regression models where the predictors are fixed and where they are stochastic are both considered. An empirical examination of the criterion and a comparison with other techniques are presented.     

A Proposal for a New Bound for Discrete Distributions

In this work we re-examine some classical bounds for non negative integer-valued random variables by means of information theoretic or maxentropic techniques using fractional moments as constraints. The proposed new bound, no more analytically expressible in terms of moments or moment generating function (mgf), is built by mixing classical bounds and the Maximum Entropy (ME) approximant of the underlying distribution; such a new bound is able to exploit optimally all the information content provided by the sequence of given moments or by the mgf. Particular care will be devoted to obtain fractional moments from the available information given in terms of integer moments and/or moment generating function. Numerical examples show clearly that the bound improvement involving the ME approximant based on fractional moments is not trivial.     

A comparison of estimation procedures for the parameters of the star model

A simulation experiment compares the accuracy and precision of three alternate estimation techniques for the parameters of the STARMA model. Maximum likelihood estimation, in most ways the "best" estimation procedure, involves a large amount of computational effort so that two approximate techniques, exact least squares and conditional maximum likelihood, are often proposed for series of moderate lengths. This simulation experiment compares the accuracy of these three estimation procedures for simulated series of various lengths, and discusses the appropriateness of the three procedures as a function of the length of the observed series.     

从“统计生态环境建设”看提高统计数据的质量

影响统计数据质量的因素是多方面的。提高统计数据质量不仅要改进统计的方法技术,还需要建设优良的统计社会环境,为统计提供良好的条件,所以应当重视“统计生态环境建设”的问题。“统计生态环境建设”包括有利于确保数据质量的思想观念环境、政府统计的体制环境、包含数据真实性的社会信用体系以及保障统计数据质量的法制环境。     

Some statistical issues in weather experimentation

A number of topics of statistical methodology in weather modification are discussed. The time sequence of unit definition, classification and randomization is shown to affect the types of units that can be used validly, and this casts doubt on the value of blocking. Re-randomization (permutation) tests are recommended as the only reliable method of confirmatory inference for weather experiments. Some aspects of such tests are examined, including a procedure for multiple comparisons. The plague of multiplicity of tests is discussed and warned against. Doubts about cumulative evaluations of "all" experiment's are expressed. A case is argued for examination of some non-randomized seeding operations. Consid¬ering the dearth of randomized data, it is argued that careful evaluation of seeding operations should be undertaken.     

A review and evaluation of the housing unit method of population estimation

"The housing unit (HU) method is used by public and private agencies throughout the United States to make local population estimates. This article describes many of the different types of data and techniques that can be used in applying the HU method, and it discusses the strengths and weaknesses of each. Empirical evidence from four different states is provided, comparing the accuracy of HU population estimates with the accuracy of other commonly used estimation techniques. Several conclusions are drawn regarding the usefulness of the HU method for local population estimation."