The aim of this study is to consider the multivariate generalized hyperbolic (MGH) distribution for modeling financial log-returns. Beginning with the multivariate geometric subordinated Brownian motion for asset pric...
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The aim of this study is to consider the multivariate generalized hyperbolic (MGH) distribution for modeling financial log-returns. Beginning with the multivariate geometric subordinated Brownian motion for asset prices, we first demonstrate that the mean-variance mixing model of the multivariate normal law is natural for log-returns of financial assets. This multivariate mean-variance mixing model forms the basis for deriving the MGH family as a class of distributions for modeling the behavior of log-returns. While theory suggests MGH to be an appropriate family, empirical considerations must also support such a proposition. This article reviews various empirical criteria in support of the MGH family. From a theoretical perspective, we present an alternative form of the density for the MGH family. This alternative density for the MGH family is more convenient for deriving certain limiting results. Numerical study on the distributional behavior of six stocks from the US market forms the foundation of investigating the suitability of the MGH family and some of its well-known subfamilies. Along the way, we implement the multicycle expectation conditional maximization algorithm for estimating the parameters of the MGH family. Then adapting a recently developed algorithmic procedure, we develop a self-contained methodology for carrying out goodness-of-fit tests for the MGH distribution. The numerical study on the six stocks confirms the suitability of the MGH distribution for different time scales of the log-returns such as daily, monthly, and 6-monthly data.
Cocaine addiction is chronic and persistent, and has become a major social and health problem in many countries. Existing studies have shown that cocaine addicts often undergo episodic periods of addiction to, moderat...
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Cocaine addiction is chronic and persistent, and has become a major social and health problem in many countries. Existing studies have shown that cocaine addicts often undergo episodic periods of addiction to, moderate dependence on, or swearing off cocaine. Given its reversible feature, cocaine use can be formulated as a stochastic process that transits from one state to another, while the impacts of various factors, such as treatment received and individuals' psychological problems on cocaine use, may vary across states. This article develops a hidden Markov latent variable model to study multivariate longitudinal data concerning cocaine use from a California Civil Addict Program. The proposed model generalizes conventional latent variable models to allow bidirectional transition between cocaine-addiction states and conventional hidden Markov models to allow latent variables and their dynamic interrelationship. We develop a maximum-likelihood approach, along with a Monte Carlo expectation conditional maximization (mcecm) algorithm, to conduct parameter estimation. The asymptotic properties of the parameter estimates and statistics for testing the heterogeneity of model parameters are investigated. The finite sample performance of the proposed methodology is demonstrated by simulation studies. The application to cocaine use study provides insights into the prevention of cocaine use.
In linear regression, a multivariate sample-selection scheme often applies to the dependent variable, which results in missing observations on the variable. This induces the sample selection bias, i.e. a standard regr...
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In linear regression, a multivariate sample-selection scheme often applies to the dependent variable, which results in missing observations on the variable. This induces the sample selection bias, i.e. a standard regression analysis using only the selected cases leads to biased results. To solve the bias problem, in this paper, we propose a class of multivariate selection regression models by extending classic Heckman model to allow for multivariate sample-selection scheme and robustness against departures from normality. Necessary theories for building a formal bias correction procedure, based upon the proposed model, are obtained, and an efficient estimation method for the model is provided. Simulation results and a real data example are presented to demonstrate the performance of the estimation method and practical usefulness of the multivariate sample-selection models. (C) 2016 The Korean Statistical Society. Published by Elsevier B.V. All rights reserved.
This article presents a generalized linear latent variable model for analyzing multivariate longitudinal data within the hidden Markov model framework. The relationships among multiple items are captured by several co...
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This article presents a generalized linear latent variable model for analyzing multivariate longitudinal data within the hidden Markov model framework. The relationships among multiple items are captured by several common latent factors. The linear coregionalization method is adopted to model the temporal processes of latent variables. The merit of this modeling strategy lies in the fact that the processes among latent variables are nonseparate and codependent from each other. To account for possible heterogeneity and interrelationship among the longitudinal data, a hidden Markov model is introduced to model the transition probabilities across different latent states over time. The Monte Carlo expectation conditional maximization (mcecm) algorithm is developed to estimate unknown parameters in the proposed model. The Wald- and score-type statistics are proposed to test the related dependence of processes. A simulation study is conducted to investigate the performance of the proposed methodology. An example from a longitudinal study of cocaine use is taken to illustrate the proposed methodology. (C) 2016 Elsevier Inc. All rights reserved.
In many practical situations, a statistical practitioner often faces a problem of classifying an object from one of the segmented (or screened) populations where the segmentation was conducted by a set of screening va...
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In many practical situations, a statistical practitioner often faces a problem of classifying an object from one of the segmented (or screened) populations where the segmentation was conducted by a set of screening variables. This paper addresses this problem, proposing and studying yet another optimal rule for classification with segmented populations. A class of q-dimensional rectangle-screened elliptically contoured (RSEC) distributions is considered for flexibly modeling the segmented populations. Based on the properties of the RSEC distributions, a parametric procedure for the segmented classification analysis (SCA) is proposed. This includes motivation for the SCA as well as some theoretical propositions regarding its optimal rule and properties. These properties allow us to establish other important results which include an efficient estimation of the rule by the Monte Carlo expectation-conditional maximization algorithm and an optimal variable selection procedure. Two numerical examples making use of utilizing a simulation study and a real dataset application and advocating the SCA procedure are also provided.
Missing data is inevitable in many situations that could hamper data analysis for scientific investigations. We establish flexible analytical tools for multivariate skew t models when fat-tailed, asymmetric and missin...
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Missing data is inevitable in many situations that could hamper data analysis for scientific investigations. We establish flexible analytical tools for multivariate skew t models when fat-tailed, asymmetric and missing observations simultaneously occur in the input data. For the ease of computation and theoretical developments, two auxiliary indicator matrices are incorporated into the model for the determination of observed and missing components of each observation that can effectively reduce the computational complexity. Under the missing at random assumption, we present a Monte Carlo version of the expectation conditional maximization algorithm, which is performed to estimate the parameters and retrieve each missing observation with a single value. Additionally, a Metropolis-Hastings within Gibbs sampler with data augmentation is developed to account for the uncertainty of parameters as well as missing outcomes. The methodology is illustrated through two real data sets.
The existing maximum likelihood theory and its computer software in structural equation modeling are established based on linear relationships among manifest variables and latent variables. However, models with nonlin...
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The existing maximum likelihood theory and its computer software in structural equation modeling are established based on linear relationships among manifest variables and latent variables. However, models with nonlinear relationships are often encountered in social and behavioral sciences. In this article, an EM type algorithm is developed for maximum likelihood estimation of a general nonlinear structural equation model. To avoid computation of the complicated multiple integrals involved, the E-step is completed by a Metropolis-Hastings algorithm. It is shown that the M-step can be completed efficiently by simple conditional maximization. Standard errors of the maximum likelihood estimates are obtained via Louis's formula. The methodology is illustrated with results from a simulation study and two real examples.
We consider the problem of maximum-likelihood estimation and smoothing for lattice processes using incomplete data. In a previous paper (Alonso et al., 1996) the authors developed a methodology based on an application...
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We consider the problem of maximum-likelihood estimation and smoothing for lattice processes using incomplete data. In a previous paper (Alonso et al., 1996) the authors developed a methodology based on an application of the EM algorithm on a state-space framework for this problem. Now, the procedure is extended using new versions of EM-type algorithms (ECM and mcecm). This has computational advantages, especially when there are many parameters to estimate. The problem of estimating the asymptotic covariance matrix for the parameter estimators is also considered (supplemented EM-type algorithms). The steps are described through an application considering the underlying state model to have an AR(1)xAR(1) structure and extension to more general models is commented on. As an example, we apply the method to the data presented by Kempton and Howes (1981).
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