“九七”前后的香港司法体制——香港政制系列研究之四

根据“港人治港”、“高度自治”的原则，香港基本法在保留香港现行司法体制中诸多成功做法的同时，赋予港人包括设立终审法院、实行司法独立在内的高度自主权。本文主要侧重于终审法院、司法独立、法官任免等的分析论证，指出“九七”后的香港司法体制在保留、吸收原有积极因素的基础上，形成与行政、立法相配套的新型政制。     

On Khatri's characterization of the inverse-Gaussian distribution

Khatri has given a characterization of the inverse-Gaussian distribution by the independence of two statistics. His proof involves assumptions on the existence of certain moments. In this note, we offer a short proof using only the positivity of the random variable X₁.     

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.     

Two-stage U-statistics for Hypothesis Testing

Abstract.  A U -statistic is not easy to apply or cannot be applied in hypothesis testing when it is degenerate or has an indeterminate degeneracy under the null hypothesis. A class of two-stage U -statistics (TU-statistics) is proposed to remedy these drawbacks. Both the asymptotic distributions under the null and the alternative of TU-statistics are shown to have simple forms. When the degeneracy is indeterminate, the Pitman asymptotic relative efficiency of a TU-statistic dominates that of the incomplete U -statistics. If the kernel is degenerate under the null hypothesis but non-degenerate under the alternative, a TU-statistic is proved to be more powerful than its corresponding U -statistic. Applications to testing independence of paired angles in ecology and marine biology are given. Finally, a simulation study shows that a TU-statistic is more powerful than its corresponding incomplete U -statistic in almost all cases under two settings.     

Causal Reasoning from Longitudinal Data*

Abstract. This paper reviews some of the key statistical ideas that are encountered when trying to find empirical support to causal interpretations and conclusions, by applying statistical methods on experimental or observational longitudinal data. In such data, typically a collection of individuals are followed over time, then each one has registered a sequence of covariate measurements along with values of control variables that in the analysis are to be interpreted as causes, and finally the individual outcomes or responses are reported. Particular attention is given to the potentially important problem of confounding. We provide conditions under which, at least in principle, unconfounded estimation of the causal effects can be accomplished. Our approach for dealing with causal problems is entirely probabilistic, and we apply Bayesian ideas and techniques to deal with the corresponding statistical inference. In particular, we use the general framework of marked point processes for setting up the probability models, and consider posterior predictive distributions as providing the natural summary measures for assessing the causal effects. We also draw connections to relevant recent work in this area, notably to Judea Pearl's formulations based on graphical models and his calculus of so‐called do‐probabilities. Two examples illustrating different aspects of causal reasoning are discussed in detail.     

我国新闻媒体监督司法审判的体制和文化障碍

现阶段,我国新闻媒体对司法审判的监督得到了进一步的加强,但我国相关体制和文化传统方面存在的一些障碍性因素,给媒体监督司法的实践带来了一系列的矛盾和负面影响,主要有:新闻媒体的官方化,法官不能做到"只服从法律"以及民众对媒体的盲信和重实体轻程序的法律文化。     

Semiparametric Efficient Estimation of the Mean of a Time Series in the Presence of Conditional Heterogeneity of Unknown Form

We obtain semiparametric efficiency bounds for estimation of a location parameter in a time series model where the innovations are stationary and ergodic conditionally symmetric martingale differences but otherwise possess general dependence and distributions of unknown form. We then describe an iterative estimator that achieves this bound when the conditional density functions of the sample are known. Finally, we develop a “semi-adaptive” estimator that achieves the bound when these densities are unknown by the investigator. This estimator employs nonparametric kernel estimates of the densities. Monte Carlo results are reported.     

On a Dualization of Graphical Gaussian Models: A Correction Note

Abstract.  We correct two proofs concerning Markov properties for graphs representing marginal independence relations.     

Goodness‐of‐fit methods for matched case‐control studies

The authors propose graphical and numerical methods for checking the adequacy of the logistic regression model for matched case‐control data. Their approach is based on the cumulative sum of residuals over the covariate or linear predictor. Under the assumed model, the cumulative residual process converges weakly to a centered Gaussian limit whose distribution can be approximated via computer simulation. The observed cumulative residual pattern can then be compared both visually and analytically to a certain number of simulated realizations of the approximate limiting process under the null hypothesis. The proposed techniques allow one to check the functional form of each covariate, the logistic link function as well as the overall model adequacy. The authors assess the performance of the proposed methods through simulation studies and illustrate them using data from a cardiovascular study.     

The k-factor GARMA Process with Infinite Variance Innovations

In this article, we develop the theory of k-factor Gegenbauer Autoregressive Moving Average (GARMA) process with infinite variance innovations which is a generalization of the stable seasonal fractional Autoregressive Integrated Moving Average (ARIMA) model introduced by Diongue et al. (2008 Diongue, A.K., Guégan, D. (2008). Estimation of k-Factor GIGARCH Process: A Monte Carlo Study. Communications in Statistics-Simulation and Computation 37:2037–2049.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]). Stationarity and invertibility conditions of this new model are derived. Conditional Sum of Squares (CSS) and Markov Chains Monte Carlo (MCMC) Whittle methods are investigated for parameter estimation. Monte Carlo simulations are also used to evaluate the finite sample performance of these estimation techniques. Finally, the usefulness of the model is corroborated with the application to streamflow data for Senegal River at Bakel.