Business-Cycle Analysis With a Markov-Switching Model

This article explores the Hamilton Markov-switching model through an analysis of the business cycles of eight developed market economies. Forecasting and specification tests suggest only marginal improvements over linear autoregressive models. Yet filtered and smoothed conditional probabilities indicate turning points in business cycles that closely correlate with turning points from traditional methods. Tests regarding the asymmetry of business cycles reject the null of symmetry for most countries.     

Bayesian prediction based on finite mixtures of lomax components model and type i censoring

This paper is concerned with the problem of obtaining Bayesian prediction bounds for future observations based on a type I censored sample from a nonhomogerieous population having a distribution which is a mixture of two Lomax components. A numerical example is given to illustrate our results.     

Some challenges for statistics

The paper gives a highly personal sketch of some current trends in statistical inference. After an account of the challenges that new forms of data bring, there is a brief overview of some topics in stochastic modelling. The paper then turns to sparsity, illustrated using Bayesian wavelet analysis based on a mixture model and metabolite profiling. Modern likelihood methods including higher order approximation and composite likelihood inference are then discussed, followed by some thoughts on statistical education.     

Bootstrap confidence intervals in mixtures of discrete distributions

The problem of building bootstrap confidence intervals for small probabilities with count data is addressed. The law of the independent observations is assumed to be a mixture of a given family of power series distributions. The mixing distribution is estimated by nonparametric maximum likelihood and the corresponding mixture is used for resampling. We build percentile-t and Efron percentile bootstrap confidence intervals for the probabilities and we prove their consistency in probability. The new theoretical results are supported by simulation experiments for Poisson and geometric mixtures. We compare percentile-t and Efron percentile bootstrap intervals with eight other bootstrap or asymptotic theory based intervals. It appears that Efron percentile bootstrap intervals outperform the competitors in terms of coverage probability and length.     

Bayesian Analysis of Multiple Hypothesis Testing with Applications to Microarray Experiments

Recently, the field of multiple hypothesis testing has experienced a great expansion, basically because of the new methods developed in the field of genomics. These new methods allow scientists to simultaneously process thousands of hypothesis tests. The frequentist approach to this problem is made by using different testing error measures that allow to control the Type I error rate at a certain desired level. Alternatively, in this article, a Bayesian hierarchical model based on mixture distributions and an empirical Bayes approach are proposed in order to produce a list of rejected hypotheses that will be declared significant and interesting for a more detailed posterior analysis. In particular, we develop a straightforward implementation of a Gibbs sampling scheme where all the conditional posterior distributions are explicit. The results are compared with the frequentist False Discovery Rate (FDR) methodology. Simulation examples show that our model improves the FDR procedure in the sense that it diminishes the percentage of false negatives keeping an acceptable percentage of false positives.     

Hidden Markov Mixture Autoregressive Models: Stability and Moments

This article introduces a parsimonious structure for mixture of autoregressive models, where the weighting coefficients are determined through latent random variables, as functions of all past observations. These latent variables follow a Markov model. We propose a dynamic programming algorithm for forecasting, which reduces the volume of calculations. We also derive limiting behavior of unconditional first moment of the process and an appropriate upper bound for the limiting value of the variance. Further more, we show convergence and stability of the second moment. Finally, we illustrate the efficacy of the proposed model by simulation.     

Estimation of the mixtures of GLMs with covariate-dependent mixing proportions

ABSTRACT

In this article, we study the estimation for a class of semiparametric mixtures of generalized linear models where mixing proportions depend on a covariate non parametrically. We investigate a backfitting estimation procedure and show the asymptotic normality of the proposed estimators under mild conditions. We conduct simulation to show the good performance of our methodology and give a real data analysis as an illustration.     

One mixed negative binomial distribution with application

In this paper we do some research on a three-parameter distribution which is called beta-negative binomial (BNB) distribution, a beta mixture of negative binomial (NB) distribution. The closed form and the factorial moment of the BNB distribution are derived. In addition, we present the recursion on the pdf of BNB stopped-sum distribution, and make stochastic comparison between BNB and NB distributions. Furthermore, we have shown that BNB distribution has heavier tail than NB distribution. The application of BNB distribution is carried out on one sample of insurance data. Based on the results, we have shown that the BNB provides a better fit compared to the Poisson and the NB for count data.     

SB-robustness of directional mean for circular distributions

In this paper we study the robustness of the directional mean (a.k.a. circular mean) for different families of circular distributions. We show that the directional mean is robust in the sense of finite standardized gross error sensitivity (SB-robust) for the following families: (1) mixture of two circular normal distributions, (2) mixture of wrapped normal and circular normal distributions and (3) mixture of two wrapped normal distributions. We also show that the directional mean is not SB-robust for the family of all circular normal distributions with varying concentration parameter. We define the circular trimmed mean and prove that it is SB-robust for this family. In general the property of SB-robustness of an estimator at a family of probability distributions is dependent on the choice of the dispersion measure. We introduce the concept of equivalent dispersion measures and prove that if an estimator is SB-robust for one dispersion measure then it is SB-robust for all equivalent dispersion measures. Three different dispersion measures for circular distributions are considered and their equivalence studied.     

Mixtures of general location model with factor analyzer covariance structure for clustering mixed type data

Cluster analysis is one of the most widely used method in statistical analyses, in which homogeneous subgroups are identified in a heterogeneous population. Due to the existence of the continuous and discrete mixed data in many applications, so far, some ordinary clustering methods such as, hierarchical methods, k-means and model-based methods have been extended for analysis of mixed data. However, in the available model-based clustering methods, by increasing the number of continuous variables, the number of parameters increases and identifying as well as fitting an appropriate model may be difficult. In this paper, to reduce the number of the parameters, for the model-based clustering mixed data of continuous (normal) and nominal data, a set of parsimonious models is introduced. Models in this set are extended, using the general location model approach, for modeling distribution of mixed variables and applying factor analyzer structure for covariance matrices. The ECM algorithm is used for estimating the parameters of these models. In order to show the performance of the proposed models for clustering, results from some simulation studies and analyzing two real data sets are presented.