An algorithm for the multivariate group lasso with covariance estimation

We study a group lasso estimator for the multivariate linear regression model that accounts for correlated error terms. A block coordinate descent algorithm is used to compute this estimator. We perform a simulation study with categorical data and multivariate time series data, typical settings with a natural grouping among the predictor variables. Our simulation studies show the good performance of the proposed group lasso estimator compared to alternative estimators. We illustrate the method on a time series data set of gene expressions.     

EM-Type algorithms for heavy-tailed logistic mixed models

This paper aims at evaluating different aspects of Monte Carlo expectation – maximization algorithm to estimate heavy-tailed mixed logistic regression (MLR) models. As a novelty it also proposes a multiple chain Gibbs sampler to generate of the latent variables distributions thus obtaining independent samples. In heavy-tailed MLR models, the analytical forms of the full conditional distributions for the random effects are unknown. Four different Metropolis–Hastings algorithms are assumed to generate from them. We also discuss stopping rules in order to obtain more efficient algorithms in heavy-tailed MLR models. The algorithms are compared through the analysis of simulated and Ascaris Suum data.     

On multivariate confidence regions and simultaneous confidence limits for ratios

Convenient general linear model computational procedures are presented for constructing multivariate confidence regions and simultaneous confidence limits for ratios of linear combinations of the parameters. The practical consequence is that a single general linear model computer program, capable of validating the underlying model and estimating the parameters, can (after slight modification) also construct the confidence regions, and even determine their precise analytic form (ellipsoid, hyperboloid, etc.). The text is deliberately factual while the appendices extend and help clarify earlier work by Henry Scheffe. As an example, a confidence ellipse and simultaneous confidence limits are constructed for several relative potencies in a classical multiple parallel line bioassay.     

Asymptotic ruin probabilities of a two-dimensional renewal risk model with dependent inter-arrival times

Abstract

This article mainly considers the uniform asymptotics for the finite-time ruin probabilities of a two-dimensional renewal risk model with heavy-tailed claims. In this model, the two claim-number processes are arbitrarily dependent and each of them is generated by widely orthant dependent claim inter-arrival times. Two types of ruin are studied and for each type of ruin, an asymptotic formula for the finite-time ruin probability is established. These formulae possess a certain uniformity feature in the time horizon.     

金融市场高维波动率的扩展广义正交GARCH模型与参数估计方法研究

本文对Van der Weide(2002)的广义正交GARCH模型进行扩展,提出反映金融资产收益波动性特征,具有"杠杆效应"的广义正交GARCH模型。由于这种扩展的广义正交GARCH模型在高维数据中面临参数估计困难,本文从交互信息理论视角研究模型的参数估计问题,在理论上证明基于交互信息最小化的多元GARCH模型参数估计与基于极大似然函数参数估计的联系和区别,并在提出的扩展广义正交GARCH模型框架下,采用不同的统计技术实现基于交互信息最小化的参数估计方法,避免了传统极大似然函数估计需要事先正确指定标准化残差概率密度函数和高维运算困难,计算效率较高,使多元GARCH模型在高维数据中可以应用。最后,根据全球主要金融市场的15种股票指数数据,通过实证研究对建立的扩展广义正交GARCH模型及其参数估计方法有效性进行评价与检验。实证研究表明了本文提出的扩展广义正交GARCH模型与参数估计方法的优势。     

Control charts for fraction nonconforming in a bivariate binomial process

Many multivariate quality control techniques are used for multivariate variable processes, but few work for multivariate attribute processes. To monitor multivariate attributes, controlling the false alarms (type I errors) and considering the correlation between attributes are two important issues. By taking into account these two issues, a new control chart is presented to monitor a bivariate binomial process. An example is illustrated for the proposed method. To evaluate the performance of the proposed method, a simulation study is conducted to compare the results with those using both the multivariate np chart and skewness reduction approaches. The results show that the correlation is taken into account in the designed chart and the overall false alarm is controlled at the nominal value. Moreover, the process shift can be quickly detected and the variable that is responsible for a signal can be determined.     

On batch queueing systems: A combinatorial approach

We consider batch queueing systems M/M^H/1$M/M^H/1$ and M^H/M/1$M^H/M/1$ with catastrophes. The transient probability functions of these queueing systems are obtained by a Lattice Path Combinatorics approach that utilizes randomization and dual processes. Steady state distributions are also determined. Generalization to systems having batches of different sizes are discussed.     

Sequential estimation of a linear function of location parameters of two negative exponential distributions

The paper considers the problem of bounded risk point estimation for a linear function of location parameters of two negative exponential distributions, including the difference in a special case, when two scale parameters are unknown. Purely sequential procedures are proposed and second order expansions of the average sample sizes and risk are given. Furthermore some simulation results are provided.