A study on model selection of binary and non-Gaussian factor analysis.

An, Yujia.Thesis (M.Phil.)--Chinese University of Hong Kong, 2005.Includes bibliographical references (leaves 71-76).Abstracts in English and Chinese.Abstract --- p.iiAcknowledgement --- p.ivChapter 1 --- Introduction --- p.1Chapter 1.1 --- Background --- p.1Chapter 1.1.1 --- Review on BFA --- p.2Chapter 1.1.2 --- Review on NFA --- p.3Chapter 1.1.3 --- Typical model selection criteria --- p.5Chapter 1.1.4 --- New model selection criterion and automatic model selection --- p.6Chapter 1.2 --- Our contributions --- p.7Chapter 1.3 --- Thesis outline --- p.8Chapter 2 --- Combination of B and BI architectures for BFA with automatic model selection --- p.10Chapter 2.1 --- Implementation of BFA using BYY harmony learning with au- tomatic model selection --- p.11Chapter 2.1.1 --- Basic issues of BFA --- p.11Chapter 2.1.2 --- B-architecture for BFA with automatic model selection . --- p.12Chapter 2.1.3 --- BI-architecture for BFA with automatic model selection . --- p.14Chapter 2.2 --- Local minima in B-architecture and BI-architecture --- p.16Chapter 2.2.1 --- Local minima in B-architecture --- p.16Chapter 2.2.2 --- One unstable result in BI-architecture --- p.21Chapter 2.3 --- Combination of B- and BI-architecture for BFA with automatic model selection --- p.23Chapter 2.3.1 --- Combine B-architecture and BI-architecture --- p.23Chapter 2.3.2 --- Limitations of BI-architecture --- p.24Chapter 2.4 --- Experiments --- p.25Chapter 2.4.1 --- Frequency of local minima occurring in B-architecture --- p.25Chapter 2.4.2 --- Performance comparison for several methods in B-architecture --- p.26Chapter 2.4.3 --- Comparison of local minima in B-architecture and BI- architecture --- p.26Chapter 2.4.4 --- Frequency of unstable cases occurring in BI-architecture --- p.27Chapter 2.4.5 --- Comparison of performance of three strategies --- p.27Chapter 2.4.6 --- Limitations of BI-architecture --- p.28Chapter 2.5 --- Summary --- p.29Chapter 3 --- A Comparative Investigation on Model Selection in Binary Factor Analysis --- p.31Chapter 3.1 --- Binary Factor Analysis and ML Learning --- p.32Chapter 3.2 --- Hidden Factors Number Determination --- p.33Chapter 3.2.1 --- Using Typical Model Selection Criteria --- p.33Chapter 3.2.2 --- Using BYY harmony Learning --- p.34Chapter 3.3 --- Empirical Comparative Studies --- p.36Chapter 3.3.1 --- Effects of Sample Size --- p.37Chapter 3.3.2 --- Effects of Data Dimension --- p.37Chapter 3.3.3 --- Effects of Noise Variance --- p.39Chapter 3.3.4 --- Effects of hidden factor number --- p.43Chapter 3.3.5 --- Computing Costs --- p.43Chapter 3.4 --- Summary --- p.46Chapter 4 --- A Comparative Investigation on Model Selection in Non-gaussian Factor Analysis --- p.47Chapter 4.1 --- Non-Gaussian Factor Analysis and ML Learning --- p.48Chapter 4.2 --- Hidden Factor Determination --- p.51Chapter 4.2.1 --- Using typical model selection criteria --- p.51Chapter 4.2.2 --- BYY harmony Learning --- p.52Chapter 4.3 --- Empirical Comparative Studies --- p.55Chapter 4.3.1 --- Effects of Sample Size on Model Selection Criteria --- p.56Chapter 4.3.2 --- Effects of Data Dimension on Model Selection Criteria --- p.60Chapter 4.3.3 --- Effects of Noise Variance on Model Selection Criteria --- p.64Chapter 4.3.4 --- Discussion on Computational Cost --- p.64Chapter 4.4 --- Summary --- p.68Chapter 5 --- Conclusions --- p.69Bibliography --- p.7

Simple techniques for likelihood analysis of univariate and multivariate stable distributions: with extensions to multivariate stochastic volatility and dynamic factor models

In this paper we consider a variety of procedures for numerical statistical inference in the family of univariate and multivariate stable distributions. In connection with univariate distributions (i) we provide approximations by finite location-scale mixtures and (ii) versions of approximate Bayesian computation (ABC) using the characteristic function and the asymptotic form of the likelihood function. In the context of multivariate stable distributions we propose several ways to perform statistical inference and obtain the spectral measure associated with the distributions, a quantity that has been a major impediment in using them in applied work. We extend the techniques to handle univariate and multivariate stochastic volatility models, static and dynamic factor models with disturbances and factors from general stable distributions, a novel way to model multivariate stochastic volatility through time-varying spectral measures and a novel way to multivariate stable distributions through copulae. The new techniques are applied to artificial as well as real data (ten major currencies, SP100 and individual returns). In connection with ABC special attention is paid to crafting well-performing proposal distributions for MCMC and extensive numerical experiments are conducted to provide critical values of the “closeness” parameter that can be useful for further applied econometric work

Simple techniques for likelihood analysis of univariate and multivariate stable distributions: with extensions to multivariate stochastic volatility and dynamic factor models

In this paper we consider a variety of procedures for numerical statistical inference in the family of univariate and multivariate stable distributions. In connection with univariate distributions (i) we provide approximations by finite location-scale mixtures and (ii) versions of approximate Bayesian computation (ABC) using the characteristic function and the asymptotic form of the likelihood function. In the context of multivariate stable distributions we propose several ways to perform statistical inference and obtain the spectral measure associated with the distributions, a quantity that has been a major impediment in using them in applied work. We extend the techniques to handle univariate and multivariate stochastic volatility models, static and dynamic factor models with disturbances and factors from general stable distributions, a novel way to model multivariate stochastic volatility through time-varying spectral measures and a novel way to multivariate stable distributions through copulae. The new techniques are applied to artificial as well as real data (ten major currencies, SP100 and individual returns). In connection with ABC special attention is paid to crafting well-performing proposal distributions for MCMC and extensive numerical experiments are conducted to provide critical values of the “closeness” parameter that can be useful for further applied econometric work

IEEE SIGNAL PROCESSING LETTERS, VOL. 11, NO. 7, JULY 2004 597 Investigations on Non-Gaussian Factor Analysis

This letter further explores the Bayesian Ying-Yang learning based non-Gaussian factor analysis (NFA) via investigating its key yet analytically intractable factor estimating step. Among the three suggested numerical approaches we empirically show that the so-called iterative fixed posteriori approximation approach is the most optimal, as well as theoretically prove that the iterative fixed posteriori approximation is another type of EM-algorithm, with the proof of its convergence also shown