A cluster‐sample approach for Monte Carlo integration using multiple samplers

A computational problem in many fields is to estimate simultaneously multiple integrals and expectations, assuming that the data are generated by some Monte Carlo algorithm. Consider two scenarios in which draws are simulated from multiple distributions but the normalizing constants of those distributions may be known or unknown. For each scenario, existing estimators can be classified as using individual samples separately or using all the samples jointly. The latter pooled‐sample estimators are statistically more efficient but computationally more costly to evaluate than the separate‐sample estimators. We develop a cluster‐sample approach to obtain computationally effective estimators, after draws are generated for each scenario. We divide all the samples into mutually exclusive clusters and combine samples from each cluster separately. Furthermore, we exploit a relationship between estimators based on samples from different clusters to achieve variance reduction. The resulting estimators, compared with the pooled‐sample estimators, typically yield similar statistical efficiency but have reduced computational cost. We illustrate the value of the new approach by two examples for an Ising model and a censored Gaussian random field. The Canadian Journal of Statistics 41: 151–173; 2013 © 2012 Statistical Society of Canada     

Nonparametric spectrum estimation for spatial data

Smoothed nonparametric kernel spectral density estimates are considered for stationary data observed on a d-dimensional lattice. The implications for edge effect bias of the choice of kernel and bandwidth are considered. Under some circumstances the bias can be dominated by the edge effect. We show that this problem can be mitigated by tapering. Some extensions and related issues are discussed.     

Adaptive estimation of error density in nonparametric regression with small sample size

It has been established recently in Efromovich [2005. Estimation of the density of regression errors. Ann. Statist. 33, 2194–2227] that, under a mild assumption, the error density in a nonparametric regression can be asymptotically estimated with the accuracy of an oracle that knows underlying regression errors. The asymptotic nature of the result, and in particular the used methodology of splitting data for estimating nuisance functions and the error density, does not make an asymptotic estimator, suggested in that article, feasible for practically interesting cases of small sample sizes. This article continues the research and solves two important issues. First, it shows that the asymptotic holds without splitting the data. Second, a data-driven estimator, based on the new asymptotic, is suggested and then tested on real and simulated examples.     

A Comparison of Rural and Urban Older Adults in Iowa on Specific Markers of Successful Aging

This study examines the differences between rural and urban older adults on level of life satisfaction and depressive symptoms, focusing on the effect of social support. Data were collected through structured interviews at senior centers and senior meal sites in eastern and southeastern Iowa. The Duke Social Support Index (DSSI), the Life Satisfaction Index-Z (LSI-Z), and the Geriatric Depression Scale 15 (GDS15) were used. Correlations (Pearson's r), independent sample t-tests, and multiple regression were computed. Findings indicated that urban residents reported more depressive symptoms, as compared to rural residents. Subjective level of social support was a stronger predictor of life satisfaction and was more negatively related to depressive symptoms among rural than among urban older adults. Results suggest that social workers who work with aging people need to be aware of rural–urban differences in mental health. Furthermore, social workers need to have knowledge of older adults' social networks and work to ensure greater opportunity for social interaction.     

Edward Gibbon Wakefield,England and 'ignorant,dirty, unsocial, . . . restless,more than half-savage' America

Abstract

Edward Gibbon Wakefield is usually credited with devising a new, 'rational' system of colonization, propounded in a series of books and articles between 1829 and 1837. Certainly, this is what his contemporary champions would have us believe but, rather than identifying what he propounds as an entirely new way of understanding colonization, it is more correct to characterize Wakefield's system as a careful decoction of existing ideas, practices and proposals trailed in earlier 19th-century British writings on the Cape, Australia, Canada and America. Published in London in 1833 and New York in 1834, England and America consequently represented a particularly selective reading of contemporary British writings on America, a highly-coloured portrayal of the country designed to demonstrate how emigration and settlement was better not conducted, and a striking contrast to his own, idealized vision of how colonies should be peopled.     

Macroeconomic imbalances in Europe: How to overcome the fallacy of unit labour costs

Policy recommendations based on unit labour costs (ULC) indices can lead to undesirable and counterproductive policies, because they do not reveal possible distortions in the base year. In this paper, we discuss the problems with the ULC-current account relation and provide an alternative measure for relative wage costs called Wage Competitive index (WCI) based on the assumption of convergence of the returns on capital. We show how to calculate it and that it is more efficient than traditional ULC and REER indicators. The implication is that policymakers should not focus on nominal wage setting only, but also more broadly on all factors which affect the return on capital. This implies that the well-known Rehn–Meidner rule, which underlies the Macroeconomic Dialogue should be modified.     

3G定制手机非恒定性附随扩散模型研究

为更科学有效地预测3G定制手机的发展趋势,为运营商提供决策依据,本文将Bass模型引入到3G定制手机扩散研究中,结合3G定制手机扩散特性,构建了非恒定性附随扩散模型。通过对基本Bass模型、附随扩散模型和非恒定附随扩散模型进行实证分析和比较分析,研究得出3G定制手机业务的非恒定性附随扩散模型的曲线拟合效果最好,适合作3G定制手机用户扩散的预测;同时,研究得出3G定制手机业务的主要扩散动力是内部影响因素,用户受口碑影响较大。因此,3G定制手机业务扩散的主要影响因素来自已采用3G定制手机的用户对潜在用户的口碑影响。     

Nonparametric hierarchical Bayes analysis of binomial data via Bernstein polynomial priors

For binomial data analysis, many methods based on empirical Bayes interpretations have been developed, in which a variance‐stabilizing transformation and a normality assumption are usually required. To achieve the greatest model flexibility, we conduct nonparametric Bayesian inference for binomial data and employ a special nonparametric Bayesian prior—the Bernstein–Dirichlet process (BDP)—in the hierarchical Bayes model for the data. The BDP is a special Dirichlet process (DP) mixture based on beta distributions, and the posterior distribution resulting from it has a smooth density defined on [0, 1]. We examine two Markov chain Monte Carlo procedures for simulating from the resulting posterior distribution, and compare their convergence rates and computational efficiency. In contrast to existing results for posterior consistency based on direct observations, the posterior consistency of the BDP, given indirect binomial data, is established. We study shrinkage effects and the robustness of the BDP‐based posterior estimators in comparison with several other empirical and hierarchical Bayes estimators, and we illustrate through examples that the BDP‐based nonparametric Bayesian estimate is more robust to the sample variation and tends to have a smaller estimation error than those based on the DP prior. In certain settings, the new estimator can also beat Stein's estimator, Efron and Morris's limited‐translation estimator, and many other existing empirical Bayes estimators. The Canadian Journal of Statistics 40: 328–344; 2012 © 2012 Statistical Society of Canada     

Bounded influence nonlinear signed‐rank regression

In this paper we consider weighted generalized‐signed‐rank estimators of nonlinear regression coefficients. The generalization allows us to include popular estimators such as the least squares and least absolute deviations estimators but by itself does not give bounded influence estimators. Adding weights results in estimators with bounded influence function. We establish conditions needed for the consistency and asymptotic normality of the proposed estimator and discuss how weight functions can be chosen to achieve bounded influence function of the estimator. Real life examples and Monte Carlo simulation experiments demonstrate the robustness and efficiency of the proposed estimator. An example shows that the weighted signed‐rank estimator can be useful to detect outliers in nonlinear regression. The Canadian Journal of Statistics 40: 172–189; 2012 © 2012 Statistical Society of Canada     

Information borrowing methods for covariate‐adjusted ROC curve

In medical diagnostic testing problems, the covariate adjusted receiver operating characteristic (ROC) curves have been discussed recently for achieving the best separation between disease and control. Due to various restrictions such as cost, the availability of patients, and ethical issues quite frequently only limited information is available. As a result, we are unlikely to have a large enough overall sample size to support reliable direct estimations of ROCs for all the underlying covariates of interest. For example, some genetic factors are less commonly observable compared with others. To get an accurate covariate adjusted ROC estimation, novel statistical methods are needed to effectively utilize the limited information. Therefore, it is desirable to use indirect estimates that borrow strength by employing values of the variables of interest from neighbouring covariates. In this paper we discuss two semiparametric exponential tilting models, where the density functions from different covariate levels share a common baseline density, and the parameters in the exponential tilting component reflect the difference among the covariates. With the proposed models, the estimated covariate adjusted ROC is much smoother and more efficient than the nonparametric counterpart without borrowing information from neighbouring covariates. A simulation study and a real data application are reported. The Canadian Journal of Statistics 40: 569–587; 2012 © 2012 Statistical Society of Canada