On Rates of Convergence for Bayesian Density Estimation

Abstract.  We consider the problem of estimating a compactly supported density taking a Bayesian nonparametric approach. We define a Dirichlet mixture prior that, while selecting piecewise constant densities, has full support on the Hellinger metric space of all commonly dominated probability measures on a known bounded interval. We derive pointwise rates of convergence for the posterior expected density by studying the speed at which the posterior mass accumulates on shrinking Hellinger neighbourhoods of the sampling density. If the data are sampled from a strictly positive, α -Hölderian density, with α  ∈ ( 0,1] , then the optimal convergence rate n^{− α / (2 α +1)} is obtained up to a logarithmic factor. Smoothing histograms by polygons, a continuous piecewise linear estimator is obtained that for twice continuously differentiable, strictly positive densities satisfying boundary conditions attains a rate comparable up to a logarithmic factor to the convergence rate n ^−4/5 for integrated mean squared error of kernel type density estimators.     

Almost Consistent Estimation of Panel Probit Models with “Small” Fixed Effects

We propose four different GMM estimators that allow almost consistent estimation of the structural parameters of panel probit models with fixed effects for the case of small Tand large N. The moments used are derived for each period from a first order approximation of the mean of the dependent variable conditional on explanatory variables and on the fixed effect. The estimators differ w.r.t. the choice of instruments and whether they use trimming to reduce the bias or not. In a Monte Carlo study, we compare these estimators with pooled probit and conditional logit estimators for different data generating processes. The results show that the proposed estimators outperform these competitors in several situations.     

Block external bootstrap in partially linear models with nonstationary strong mixing error terms

The authors extend the block external bootstrap to partially linear regression models with strongly mixing, nonstationary error terms. In addition to providing an approximate distribution for the semiparametric least square estimator of the parametric component, they propose a consistent estimator of the co‐variance matrix of this estimator.     

A Non-parametric Frailty Model for Temporally Clustered Multivariate Failure Times

Abstract A model is introduced here for multivariate failure time data arising from heterogenous populations. In particular, we consider a situation in which the failure times of individual subjects are often temporally clustered, so that many failures occur during a relatively short age interval. The clustering is modelled by assuming that the subjects can be divided into ‘internally homogenous’ latent classes, each such class being then described by a time‐dependent frailty profile function. As an example, we reanalysed the dental caries data presented earlier in Härkänen et al. [Scand. J. Statist. 27 (2000) 577], as it turned out that our earlier model could not adequately describe the observed clustering.     

Complex belief-desire reasoning in children

Previous research concerned with children's belief-desire psychology has examined the capacity to predict or interpret action on the basis of the implicit proposition that ‘when an actor desires a particular end and believes that a particular action will achieve that end, he or she will undertake that action’. The limitations of this formulation for understanding acts of omission are outlined and an elaborated version of belief-desire psychology introduced. This version holds that ‘when an actor desires a particular end and believes that a particular action will achieve that end, and when it is believed that there are no co-occurring outcomes of that action whose avoidance is desired more highly than is the originally conceived end, then the actor will undertake the action which will satisfy the original desire’. An experiment is reported which examines 4-, 5, and 7-year-olds' ability to predict story characters' actions on the basis of either their true or false beliefs concerning undesirable outcomes associated with the pursuit of a desired end. Children of all age-groups provided evidence of understanding the elaborated version of belief-desire psychology. However, a significant improvement was noted between the ages of 4 and 7 years in the ability to understand circumstances involving false beliefs.     

A Unified Approach to the Characterization of Equivalence Classes of DAGs, Chain Graphs with no Flags and Chain Graphs

Abstract.  A Markov property associates a set of conditional independencies to a graph. Two alternative Markov properties are available for chain graphs (CGs), the Lauritzen–Wermuth–Frydenberg (LWF) and the Andersson–Madigan– Perlman (AMP) Markov properties, which are different in general but coincide for the subclass of CGs with no flags . Markov equivalence induces a partition of the class of CGs into equivalence classes and every equivalence class contains a, possibly empty, subclass of CGs with no flags itself containing a, possibly empty, subclass of directed acyclic graphs (DAGs). LWF-Markov equivalence classes of CGs can be naturally characterized by means of the so-called largest CGs , whereas a graphical characterization of equivalence classes of DAGs is provided by the essential graphs . In this paper, we show the existence of largest CGs with no flags that provide a natural characterization of equivalence classes of CGs of this kind, with respect to both the LWF- and the AMP-Markov properties. We propose a procedure for the construction of the largest CGs, the largest CGs with no flags and the essential graphs, thereby providing a unified approach to the problem. As by-products we obtain a characterization of graphs that are largest CGs with no flags and an alternative characterization of graphs which are largest CGs. Furthermore, a known characterization of the essential graphs is shown to be a special case of our more general framework. The three graphical characterizations have a common structure: they use two versions of a locally verifiable graphical rule. Moreover, in case of DAGs, an immediate comparison of three characterizing graphs is possible.     

人力资源开发与高校办学定位

教育是人力资源开发的主导形式,高校办学定位直接影响着人才培养的类型和规格。适应科学技术的发展和社会经济增长方式的转变,高校办学定位必须与时俱进,不断调整和革新。在当前和今后相当长一段时间,高师院校必须走“以师为本、综合发展”之路。     

Progress and cumulation in the human sciences after the fall

What do we mean by progress and cumulation in the social and human sciences? Recent thinking in the philosophy and history of science has led to an abandonment of some versions of logical positivism and of verificationism that had a strong deductive and theory testing orientation. What is to replace them is less clear. This paper argues that progress and cumulation can be seen as a process of evaluation and retention within an epistemic community. Scholarly disciplines differ in their social structure and in their epistemic and normative commitments. Since sociology is a fragmented discipline, progress and cumulation differ within its multiple subdisciplines, which to varying extents represent epistemic communities. Brief sketches of progress (advance) and cumulation in several subdisciplines are offered.     

Mapping water quality by local scoring

The mean density of bacteria in a water body is commonly monitored using quantal assay. This paper describes the use of local scoring in estimating the spatial distribution of mean density from quantal assay results at a set of point locations. An application to estimating the mean density of fecal conform bacteria in a coastal pond is presented. Model diagnostics based on a parametric bootstrap are also presented.     

First Nations and community economic development: a case study

A training project in a northern Canadian community providedan opportunity to examine participatory planning approachesand the meaning of work in First Nations communities. Focusgroups conducted three years after the unsuccessful interventionof a community economic development (CED) project suggest thatcomplex factors such as lack of support from community leadersand rate of pay for workers determine whether CED is alwaysappropriate in northern, First Nations contexts.