On constructing sequences estimating the mixing distribution with applications

This paper shows that by minimizing a Chebychev norm a mixing distribution can be constructed which converges weakly to the true mixing distribution with probability one. Deely and Kruse (1968) established a similar result for the supremum norm. For both norms the constructed mixing distribution is computed by solving a linear programming problem, but this problem is considerably smaller when the Chebychev norm is used. Thus a suitable mixing distribution can be constructed from solving a linear programming problem with considerably less computational work than was previously known. To illustrate the application of this simpler procedure it is applied to derive nonparametric empirical Bayes estimates in a simulation study. Some density estimates are also illustrated.     

Further influence measures in factor analysis

Various influence measures are discussed for sensitivity analysis in factor analysis. The internal norm is used to characterize the vector-valued influence curves in factor analysis. Influence curves for the chi-square goodness of fit test, and the determinants of the model covariance matrix and unique variance matrix are derived. They are found to have simple formulas which are easy to be interpreted and have nice distributions for calibration. The likelihood displacement is also applied to sensitivity analysis in maximum likelihood factor analysis.     

Computation of determinantal subset influence in regression

One of the important goals of regression diagnostics is the detection of cases or groups of cases which have an inordinate impact on the regression results. Such observations are generally described as influential. A number of influence measures have been proposed, each focusing on a different aspect of the regression. For single cases, these measures are relatively simple and inexpensive to calculate. However, the detection of multiple-case or joint influence is more difficult on two counts. First, calculation of influence for a single subset is more involved than for an individual case, and second, the sheer number of subsets of cases makes the computation overwhelming for all but the smallest data sets.Barrett and Gray (1992) described methods for efficiently examining subset influence for those measures that can be expressed as the trace of a product of positive semidefinite (psd) matrices. There are, however, other popular measures that do not take this form, but rather are expressible as the ratio of determinants of psd matrices. This article focuses on reducing the computation for the determinantal ratio measures by making use of upper and lower bounds on the influence to limit the number of subsets for which the actual influence must be explicitly determined.     

Robust m-estimators

This paper provides a summary of the influence function approach to robust estimation of parametric models. Hampel's optimality results for M-estimators with a bounded influence function is generalized to allow for arbitrary choices of the asymptotic efficiency criterion and the norm of the influence function. Further extensions to other cases of practical interest are also considered.     

女性家庭地位越高就越幸福吗?

人们普遍认为,女性家庭地位越高就会越幸福。然而,本文使用中国家庭追踪调查数据,基于有序响应模型和条件混合过程法,研究发现女性拥有更多家庭事务决策权未必能改善其幸福感。分样本回归显示,对于受教育少以及受强外部传统文化规范约束的女性群体,家庭决策权对其幸福感的负向影响尤为显著。这一发现,对将来关于个体幸福感的研究具有重要启示,即只有把外部文化规范等社会背景考虑进来,家庭决策者身份的幸福效应方向才能最终确认。此外,本文关于传统文化规范力量 仍然主导着女性幸福感的发现,也为政府部门制定致力于赋权女性的政策提供了论证基点。     

A comparison of regression calibration approaches for designs with internal validation data

We compare the asymptotic relative efficiency of several regression calibration methods of correcting for measurement error in studies with internal validation data, when a single covariate is measured with error. The estimators we consider are appropriate in main study/hybrid validation study designs, where the latter study includes internal validation and may include external validation data. Although all of the methods we consider produce consistent estimates, the method proposed by Spiegelman et al. (Statistics in Medicine, 20 (2001) 139) has an asymptotically smaller variance than the other methods. The methods for measurement error correction are illustrated using a study of the effect of in utero lead exposure on infant birth weight.     

A bounded influence regression estimator based on the statistics of the hat matrix

Summary. Many geophysical regression problems require the analysis of large (more than 10⁴ values) data sets, and, because the data may represent mixtures of concurrent natural processes with widely varying statistical properties, contamination of both response and predictor variables is common. Existing bounded influence or high breakdown point estimators frequently lack the ability to eliminate extremely influential data and/or the computational efficiency to handle large data sets. A new bounded influence estimator is proposed that combines high asymptotic efficiency for normal data, high breakdown point behaviour with contaminated data and computational simplicity for large data sets. The algorithm combines a standard M -estimator to downweight data corresponding to extreme regression residuals and removal of overly influential predictor values (leverage points) on the basis of the statistics of the hat matrix diagonal elements. For this, the exact distribution of the hat matrix diagonal elements p _ii for complex multivariate Gaussian predictor data is shown to be β ( p _ii ,  m ,  N − m ), where N is the number of data and m is the number of parameters. Real geophysical data from an auroral zone magnetotelluric study which exhibit severe outlier and leverage point contamination are used to illustrate the estimator's performance. The examples also demonstrate the utility of looking at both the residual and the hat matrix distributions through quantile–quantile plots to diagnose robust regression problems.     

产业关联测度方法的改进及应用——基于OECD非竞争型投入产出表的分析

影响力系数是产业关联测度中重要的分析工具,然而影响力系数的传统测算公式存在诸多缺陷。综述了影响力系数的传统测算公式中存在的主要缺陷;在此基础上综合考虑了产业结构(份额)、衡量标准以及中间投入的国内外区分等因素,对影响力系数的传统测算公式进行了改进;在中国的非竞争型投入产出表的基础上,比较分析了影响力系数测算公式改进前后计算结果的差异。     

Influence analysis of additive mixed-effects nonlinear regression models via EM algorithm

This paper presents a unified method for influence analysis to deal with random effects appeared in additive nonlinear regression models for repeated measurement data. The basic idea is to apply the Q-function, the conditional expectation of the complete-data log-likelihood function obtained from EM algorithm, instead of the observed-data log-likelihood function as used in standard influence analysis. Diagnostic measures are derived based on the case-deletion approach and the local influence approach. Two real examples and a simulation study are examined to illustrate our methodology.     

Relative local influence and the condition number

In this paper we show that the condition number traditionally used by numerical analysts is closely related to a variant of Cook's (1986) absolute measure of local influence. The nature of the assumptions made in our derivation of this result raises several questions concerning the relevance of the traditional condition number as a measure of computational accuracy in statistical studies.     

Local influence analysis for regression models with scale mixtures of skew-normal distributions

The robust estimation and the local influence analysis for linear regression models with scale mixtures of multivariate skew-normal distributions have been developed in this article. The main virtue of considering the linear regression model under the class of scale mixtures of skew-normal distributions is that they have a nice hierarchical representation which allows an easy implementation of inference. Inspired by the expectation maximization algorithm, we have developed a local influence analysis based on the conditional expectation of the complete-data log-likelihood function, which is a measurement invariant under reparametrizations. This is because the observed data log-likelihood function associated with the proposed model is somewhat complex and with Cook's well-known approach it can be very difficult to obtain measures of the local influence. Some useful perturbation schemes are discussed. In order to examine the robust aspect of this flexible class against outlying and influential observations, some simulation studies have also been presented. Finally, a real data set has been analyzed, illustrating the usefulness of the proposed methodology.     

Further theoretical results and a comparison between two methods for approximating eigenvalues of perturbed covariance matrices

Covariance matrices, or in general matrices of sums of squares and cross-products, are used as input in many multivariate analyses techniques. The eigenvalues of these matrices play an important role in the statistical analysis of data including estimation and hypotheses testing. It has been recognized that one or few observations can exert an undue influence on the eigenvalues of a covariance matrix. The relationship between the eigenvalues of the covariance matrix computed from all data and the eigenvalues of the perturbed covariance matrix (a covariance matrix computed after a small subset of the observations has been deleted) cannot in general be written in closed-form. Two methods for approximating the eigenvalues of a perturbed covariance matrix have been suggested by Hadi (1988) and Wang and Nyquist (1991) for the case of a perturbation by a single observation. In this paper we improve on these two methods and give some additional theoretical results that may give further insight into the problem. We also compare the two improved approximations in terms of their accuracies.     

Influence Assessment in an Heteroscedastic Errors-in-Variables Model

The main goal of this article is to consider influence assessment in models with error-prone observations and variances of the measurement errors changing across observations. The techniques enable to identify potential influential elements and also to quantify the effects of perturbations in these elements on some results of interest. The approach is illustrated with data from the WHO MONICA Project on cardiovascular disease.     

城市化与中国碳排放的实证研究

中国的经济增长模式正从外需增长转向内需增长,而内需增长的核心是建立在城市化基础上的,城市化已成为中国经济持续增长的另一引擎。为反映城市化对CO2排放的影响,利用STIRPAT模型研究1978—2010年期间不同发展阶段的东中西区域城市化对于碳排放的影响与效应。研究发现:对处于不同发展阶段的三个样本,城市化水平对各省碳排放均为正相关关系,说明中国经济在快速增长阶段城市化的推进带来了碳排放的增加,但这种正相关的关系并不显著,因城市化的进程会引起环境问题,进一步的城市化则慢慢消除了环境问题;无论是东部、中部还是西部地区,人均收入与碳排放、碳强度与碳排放的关系显著为正。鉴此,减排的重点在于降低碳强度,并可通过技术进步和能源结构的变迁减少碳排放。     

Model Selection for Vector Autoregressive Processes via Adaptive Lasso

Determination of the best subset is an important step in vector autoregressive (VAR) modeling. Traditional methods either conduct subset selection and parameter estimation separately or compute expensively. In this article, we propose a VAR model selection procedure using adaptive Lasso, for it is computational efficient and can select subset and estimate parameters simultaneously. By proper choice of tuning parameters, we can choose the correct subset and obtain the asymptotic normality of the non zero parameters. Simulation studies and real data analysis show that adaptive Lasso performs better than existing methods in VAR model fitting and prediction.     

基于ESDA-GWR的三重城镇化协调性空间分异及驱动力研究

城镇化协调发展是提升我国城镇化质量的基本前提。在界定三重城镇化概念的基础上,构建人口、资本和土地城镇化协调发展的测度指标,利用复合系统耦合协调度模型评价我国283个地级市三重城镇化的协调发展水平,并分别应用探索性空间数据分析和地理加权回归模型,研究三重城镇化的空间分布及其内、外驱动力。研究发现,我国地级市尺度的三重城镇化协调度整体有所提升,但不同地区差异明显,且存在空间相关;在影响三重城镇化协调度的各类因素中,内部驱动力占主导地位,外部驱动力的影响较弱,人口-资本城镇化和资本-土地城镇化协调是促使三重城镇化协调的中坚力量,而人口与土地城镇化的失衡则导致了三重城镇化的失调。     

Sparse Bayesian variable selection in multinomial probit regression model with application to high-dimensional data classification

Here we consider a multinomial probit regression model where the number of variables substantially exceeds the sample size and only a subset of the available variables is associated with the response. Thus selecting a small number of relevant variables for classification has received a great deal of attention. Generally when the number of variables is substantial, sparsity-enforcing priors for the regression coefficients are called for on grounds of predictive generalization and computational ease. In this paper, we propose a sparse Bayesian variable selection method in multinomial probit regression model for multi-class classification. The performance of our proposed method is demonstrated with one simulated data and three well-known gene expression profiling data: breast cancer data, leukemia data, and small round blue-cell tumors. The results show that compared with other methods, our method is able to select the relevant variables and can obtain competitive classification accuracy with a small subset of relevant genes.     

Specifying a Gaussian Markov Random Field by a Sparse Cholesky Triangle

ABSTRACT

This note discusses the approach of specifying a Gaussian Markov random field (GMRF) by the Cholesky triangle of the precision matrix. A such representation can be made extremely sparse using numerical techniques for incomplete sparse Cholesky factorization, and provide very computational efficient representation for simulating from the GMRF. However, we provide theoretical and empirical justification showing that the sparse Cholesky triangle representation is fragile when conditioning a GMRF on a subset of the variables or observed data, meaning that the computational cost increases.     

Analysis of inaccurate data with mixture measurement error models

Measurement error, the difference between a measured (observed) value of quantity and its true value, is perceived as a possible source of estimation bias in many surveys. To correct for such bias, a validation sample can be used in addition to the original sample for adjustment of measurement error. Depending on the type of validation sample, we can either use the internal calibration approach or the external calibration approach. Motivated by Korean Longitudinal Study of Aging (KLoSA), we propose a novel application of fractional imputation to correct for measurement error in the analysis of survey data. The proposed method is to create imputed values of the unobserved true variables, which are mis-measured in the main study, by using validation subsample. Furthermore, the proposed method can be directly applicable when the measurement error model is a mixture distribution. Variance estimation using Taylor linearization is developed. Results from a limited simulation study are also presented.     

Maximum-likelihood estimation and influence analysis in multivariate skew-normal reproductive dispersion mixed models for longitudinal data

Various mixed models were developed to capture the features of between- and within-individual variation for longitudinal data under the normality assumption of the random effect and the within-individual random error. However, the normality assumption may be violated in some applications. To this end, this article assumes that the random effect follows a skew-normal distribution and the within-individual error is distributed as a reproductive dispersion model. An expectation conditional maximization (ECME) algorithm together with the Metropolis-Hastings (MH) algorithm within the Gibbs sampler is presented to simultaneously obtain estimates of parameters and random effects. Several diagnostic measures are developed to identify the potentially influential cases and assess the effect of minor perturbation to model assumptions via the case-deletion method and local influence analysis. To reduce the computational burden, we derive the first-order approximations to case-deletion diagnostics. Several simulation studies and a real data example are presented to illustrate the newly developed methodologies.