Modeling heavy-tailed,skewed and peaked uncertainty phenomena with bounded support

A prevalence of heavy-tailed, peaked and skewed uncertainty phenomena have been cited in literature dealing with economic, physics, and engineering data. This fact has invigorated the search for continuous distributions of this nature. In this paper we shall generalize the two-sided framework presented in Kotz and van Dorp (Beyond beta: other continuous families of distributions with bounded support and applications. World Scientific Press, Singapore, 2004) for the construction of families of distributions with bounded support via a mixture technique utilizing two generating densities instead of one. The family of Elevated Two-Sided Power (ETSP) distributions is studied as an instance of this generalized framework. Through a moment ratio diagram comparison, we demonstrate that the ETSP family allows for a remarkable flexibility when modeling heavy-tailed and peaked, but skewed, uncertainty phenomena. We shall demonstrate its applicability via an illustrative example utilizing 2008 US income data.     

Lag Length Selection for Unit Root Tests in the Presence of Nonstationary Volatility

A number of recent papers have focused on the problem of testing for a unit root in the case where the driving shocks may be unconditionally heteroskedastic. These papers have, however, taken the lag length in the unit root test regression to be a deterministic function of the sample size, rather than data-determined, the latter being standard empirical practice. We investigate the finite sample impact of unconditional heteroskedasticity on conventional data-dependent lag selection methods in augmented Dickey–Fuller type regressions and propose new lag selection criteria which allow for unconditional heteroskedasticity. Standard lag selection methods are shown to have a tendency to over-fit the lag order under heteroskedasticity, resulting in significant power losses in the (wild bootstrap implementation of the) augmented Dickey–Fuller tests under the alternative. The proposed new lag selection criteria are shown to avoid this problem yet deliver unit root tests with almost identical finite sample properties as the corresponding tests based on conventional lag selection when the shocks are homoskedastic.     

Bayesian quantile regression for single-index models

Using an asymmetric Laplace distribution, which provides a mechanism for Bayesian inference of quantile regression models, we develop a fully Bayesian approach to fitting single-index models in conditional quantile regression. In this work, we use a Gaussian process prior for the unknown nonparametric link function and a Laplace distribution on the index vector, with the latter motivated by the recent popularity of the Bayesian lasso idea. We design a Markov chain Monte Carlo algorithm for posterior inference. Careful consideration of the singularity of the kernel matrix, and tractability of some of the full conditional distributions leads to a partially collapsed approach where the nonparametric link function is integrated out in some of the sampling steps. Our simulations demonstrate the superior performance of the Bayesian method versus the frequentist approach. The method is further illustrated by an application to the hurricane data.     

Combinatoric classification of multivariate normal variates

Consider classifying an n × I observation vector as coming from one of two multivariate normal distributions which differ both in mean vectors and covariance matrices. A class of dis-crimination rules based upon n independent univariate discrim-inate functions is developed yielding exact misclassification probabilities when the population parameters are known. An efficient search of this class to select the procedure with minimum expected misclassification is made by employing an algorithm of the implicit enumeration type used in integer programming. The procedure is applied to the classification of male twins as either monozygotic or dizygotic.     

A time series model with random coefficients

There are many time series applications where an experi­menter observes the simultaneous responses of several sub­systems over time. In these instances one is often not interested in the parameters of individual subsystems, but rather in an overall characterization of the system in question. Under the assumption that subsystems are independent and first order autoregressive, the present paper presents two methods for estimating the distribution of the subsystem coefficients.     

Standard and goodness-of-fit parameter estimation methods for the three-parameter lognormal distribution

A class of goodness-of-fit estimators is found to provide a useful alternative in certain situations to the standard maximum likelihood method which has some undesirable estimation characteristics for estimation from the three-parameter lognormal distribution. The class of goodness-of-fit tests considered include the Shapiro-Wilk and Filliben tests which reduce to a weighted linear combination of the order statistics that can be maximized in estimation problems. The weighted order statistic estimators are compared to the standard procedures in Monte Carlo simulations. Robustness of the procedures are examined and example data sets analyzed.     

Exact moments of a ratio of two positive quadratic forms in normal variables

This paper derives an expression for rth raw moment of aratio of two quadratic forms in normal variables in terms of' a

convergent infinite series. Computational aspects of this formula are explored by considering a particular case.