Simplex Mixed‐Effects Models for Longitudinal Proportional Data

Abstract. Continuous proportional outcomes are collected from many practical studies, where responses are confined within the unit interval (0,1). Utilizing Barndorff‐Nielsen and Jørgensen's simplex distribution, we propose a new type of generalized linear mixed‐effects model for longitudinal proportional data, where the expected value of proportion is directly modelled through a logit function of fixed and random effects. We establish statistical inference along the lines of Breslow and Clayton's penalized quasi‐likelihood (PQL) and restricted maximum likelihood (REML) in the proposed model. We derive the PQL/REML using the high‐order multivariate Laplace approximation, which gives satisfactory estimation of the model parameters. The proposed model and inference are illustrated by simulation studies and a data example. The simulation studies conclude that the fourth order approximate PQL/REML performs satisfactorily. The data example shows that Aitchison's technique of the normal linear mixed model for logit‐transformed proportional outcomes is not robust against outliers.     

Estimation method of multivariate exponential probabilities based on a simplex coordinates transform

A novel unbiased estimator for estimating the probability mass of a multivariate exponential distribution over a measurable set is introduced and is called the exponential simplex (ES) estimator. For any measurable set and given sample size, the statistical efficiency of the ES estimator is higher than or equal to the statistical efficiency of the well-known Monte Carlo (MC) estimator. For non-radially shaped measurable sets, the ES estimator has a strictly higher statistical efficiency than the MC estimator. For ray-convex sets, such as convex sets, the ES estimator can be expressed in a simple analytical form.     

Conditional Extremes in Asymmetric Financial Markets

ABSTRACT

The global financial crisis of 2007–2009 revealed the great extent to which systemic risk can jeopardize the stability of the entire financial system. An effective methodology to quantify systemic risk is at the heart of the process of identifying the so-called systemically important financial institutions for regulatory purposes as well as to investigate key drivers of systemic contagion. The article proposes a method for dynamic forecasting of CoVaR, a popular measure of systemic risk. As a first step, we develop a semi-parametric framework using asymptotic results in the spirit of extreme value theory (EVT) to model the conditional probability distribution of a bivariate random vector given that one of the components takes on a large value, taking into account important features of financial data such as asymmetry and heavy tails. In the second step, we embed the proposed EVT method into a dynamic framework via a bivariate GARCH process. An empirical analysis is conducted to demonstrate and compare the performance of the proposed methodology relative to a very flexible fully parametric alternative.     

规则框架的一种实用简化计算方法

近年来，钢筋混凝土框架结构的应用越来越广泛，在一般工业与民用建筑中，规则框架所占的比例很高，因此合理解决规则框架的简化计算有较大的意义．本文所介绍的规则框架的简化计算方法，对工程实际具有一定的指导意义．     

An algorithm for optimal designs on a design space

Two variations of a simple monotunic algorithm for computing optimal designs on a finite design space are presented. Various properties are listed. Comparisons witn other algorithms are made.     

Robustness and monotonicity properties of generalized correlation coefficients

A new class of generalized correlation coefficients that contains the Pearson and Kendall statistics as special cases was defined by Chinchilli et al. (2005) and applied to the estimation of correlations coefficients within the context of 2×2 cross-over designs for clinical trials. In this paper, we determine the infinitesimal robustness and local stability properties of these generalized correlation coefficients by deriving their corresponding influence functions. For cases in which the population distribution is a bivariate normal or a mixture of bivariate normal distributions we obtain explicit formulas, and establish monotonicity and sign-reverse rule properties of the generalized correlation coefficients.     

On a class of distributions on the simplex

In the present paper we define and investigate a novel class of distributions on the simplex, termed normalized infinitely divisible distributions, which includes the Dirichlet distribution. Distributional properties and general moment formulae are derived. Particular attention is devoted to special cases of normalized infinitely divisible distributions which lead to explicit expressions. As a by-product new distributions over the unit interval and a generalization of the Bessel function distribution are obtained.     

论汉字的构形理据及其演变

汉字初创时的象形特征非常明显,后随着社会的发展变化,汉字字体不断改变,由甲骨文至金文至小篆,其象形特征日渐消失;汉字字体演变为隶书、楷书后,其象形特征基本消失。在字体的演变过程中,汉字的笔画形态、部件的组合关系均有不同程度的改变,甚至是部分汉字的意义发生了不同性质的变化;这些变化不可避免地影响到汉字的构形理据,并使其产生某种程度的改变。考察我国目前使用的通行字,我们发现,它们有的完全保留了汉字初创时的构形理据,有的部分保留,有的丢失了构形理据,有的则根本找不到构形理据。构形理据的保留或部分保留是汉字发展演变的必然,但构形理据的丧失或根本找不到构形理据则与人为地改造汉字、构造新字有关。     

NUMBERS OF OBSERVATIONS NEAR ORDER STATISTICS

Limit theorems are obtained for the numbers of observations in a random sample that fall within a left‐hand or right‐hand neighbourhood of the kth order statistic. The index k can be fixed, or tend to infinity as the sample size increases unboundedly. In essence, the proofs are applications of the classical Poisson and De Moivre–Laplace theorems.