Bayes linear analysis for graphical models: The geometric approach to local computation and interpretive graphics

This paper concerns the geometric treatment of graphical models using Bayes linear methods. We introduce Bayes linear separation as a second order generalised conditional independence relation, and Bayes linear graphical models are constructed using this property. A system of interpretive and diagnostic shadings are given, which summarise the analysis over the associated moral graph. Principles of local computation are outlined for the graphical models, and an algorithm for implementing such computation over the junction tree is described. The approach is illustrated with two examples. The first concerns sales forecasting using a multivariate dynamic linear model. The second concerns inference for the error variance matrices of the model for sales, and illustrates the generality of our geometric approach by treating the matrices directly as random objects. The examples are implemented using a freely available set of object-oriented programming tools for Bayes linear local computation and graphical diagnostic display.     

台湾师范教育变革之趋势

１９９５ 年后,台湾的师资培育工作已由师范院校扩及到一般的大学院校,从而使台湾的师范院校面临着很大的冲击。为了不致于在师资培育方面失去其重要地位,台湾的师范院校都采取了应对性策略。今后,台湾师范院校将以向综合大学转型作为主要的发展趋势。     

综合业务CATV网络

本文提出了一种宽带分布式网络设计,该网络能在CATV电缆上同时进行数据、实时数字话音及模拟电视通信。本系统能支持大量用户间的通信。由于采用了宽带技术和总线网令牌与CSMA/CD的混合协议,从而解决了局域网所面临的距离和时延问题。本文最后对所提出网络的话音性能作了评估,所得结果与相关试验报导数据相符。     

Local Power Analyses of Goodness-of-fit Tests for Copulas

Abstract.  The asymptotic behaviour of several goodness-of-fit statistics for copula families is obtained under contiguous alternatives. Many comparisons between a Cramér–von Mises functional of the empirical copula process and new moment-based goodness-of-fit statistics are made by considering their associated asymptotic local power curves. It is shown that the choice of the estimator for the unknown parameter can have a significant influence on the power of the Cramér–von Mises test and that some of the moment-based statistics can provide simple and efficient goodness-of-fit methods.     

Least squares estimation of varying‐coefficient hazard regression with application to breast cancer dose‐intensity data

To enhance modeling flexibility, the authors propose a nonparametric hazard regression model, for which the ordinary and weighted least squares estimation and inference procedures are studied. The proposed model does not assume any parametric specifications on the covariate effects, which is suitable for exploring the nonlinear interactions between covariates, time and some exposure variable. The authors propose the local ordinary and weighted least squares estimators for the varying‐coefficient functions and establish the corresponding asymptotic normality properties. Simulation studies are conducted to empirically examine the finite‐sample performance of the new methods, and a real data example from a recent breast cancer study is used as an illustration. The Canadian Journal of Statistics 37: 659–674; 2009 © 2009 Statistical Society of Canada     

The marked empirical process to test nonlinear time series against a large class of alternatives when the random vectors are nonstationary and absolutely regular

In this paper, we propose a method for testing absolutely regular and possibly nonstationary nonlinear time-series, with application to general AR-ARCH models. Our test statistic is based on a marked empirical process of residuals which is shown to converge to a Gaussian process with respect to the Skohorod topology. This testing procedure was first introduced by Stute [Nonparametric model checks for regression, Ann. Statist. 25 (1997), pp. 613–641] and then widely developed by Ngatchou-Wandji [Weak convergence of some marked empirical processes: Application to testing heteroscedasticity, J. Nonparametr. Stat. 14 (2002), pp. 325–339; Checking nonlinear heteroscedastic time series models, J. Statist. Plann. Inference 133 (2005), pp. 33–68; Local power of a Cramer-von Mises type test for parametric autoregressive models of order one, Compt. Math. Appl. 56(4) (2008), pp. 918–929] under more general conditions. Applications to general AR-ARCH models are given.     

Statistical inference on asymptotic properties of two estimators for the partially linear single-index models

The outer product of gradients (OPG) estimation procedure based on least squares (LS) approach has been presented by Xia et al. [An adaptive estimation of dimension reduction space. J Roy Statist Soc Ser B. 2002;64:363–410] to estimate the single-index parameter in partially linear single-index models (PLSIM). However, its asymptotic property has not been established yet and the efficiency of LS-based method can be significantly affected by outliers and heavy-tailed distributions. In this paper, we firstly derive the asymptotic property of OPG estimator developed by Xia et al. [An adaptive estimation of dimension reduction space. J Roy Statist Soc Ser B. 2002;64:363–410] in theory, and a novel robust estimation procedure combining the ideas of OPG and local rank (LR) inference is further developed for PLSIM along with its theoretical property. Then, we theoretically derive the asymptotic relative efficiency (ARE) of the proposed LR-based procedure with respect to LS-based method, which is shown to possess an expression that is closely related to that of the signed-rank Wilcoxon test in comparison with the t-test. Moreover, we demonstrate that the new proposed estimator has a great efficiency gain across a wide spectrum of non-normal error distributions and almost not lose any efficiency for the normal error. Even in the worst case scenarios, the ARE owns a lower bound equalling to 0.864 for estimating the single-index parameter and a lower bound being 0.8896 for estimating the nonparametric function respectively, versus the LS-based estimators. Finally, some Monte Carlo simulations and a real data analysis are conducted to illustrate the finite sample performance of the estimators.     

Tests of hypotheses based on ranks in the general linear model

A unified approach is developed for testing hypotheses in the general linear model based on the ranks of the residuals. It complements the nonparametric estimation procedures recently reported in the literature. The testing and estimation procedures together provide a robust alternative to least squares. The methods are similar in spirit to least squares so that results are simple to interpret. Hypotheses concerning a subset of specified parameters can be tested, while the remaining parameters are treated as nuisance parameters. Asymptotically, the test statistic is shown to have a chi-square distribution under the null hypothesis. This result is then extended to cover a sequence of contiguous alternatives from which the Pitman efficacy is derived. The general application of the test requires the consistent estimation of a functional of the underlying distribution and one such estimate is furnished.