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In this work, we derive the copulas related to vectors obtained from the so-called chaotic stochastic processes. These are defined by the iteration of certain piecewise monotone functions of the interval [0, 1] to some initial random variable. We study some of its properties and present some examples. Since often these types of copulas do not have closed formulas, we provide a general approximation method which converges uniformly to the true copula. Our results cover a wide class of processes, including the so-called Manneville–Pomeau processes. The general theory is applied to the parametric estimation in certain chaotic processes. A Monte Carlo simulation study is also presented. [ABSTRACT FROM PUBLISHER]

Bayesian inference for fractionally integrated exponential generalized autoregressive conditional heteroscedastic (FIEGARCH) models using Markov chain Monte Carlo (MCMC) methods is described. A simulation study is presented to assess the performance of the procedure, under the presence of long-memory in the volatility. Samples from FIEGARCH processes are obtained upon considering the generalized error distribution (GED) for the innovation process. Different values for the tail-thickness parameter ν are considered covering both scenarios, innovation processes with lighter (ν > 2) and heavier (ν < 2) tails than the Gaussian distribution (ν = 2). A comparison between the performance of quasi-maximum likelihood (QML) and MCMC procedures is also discussed. An application of the MCMC procedure to estimate the parameters of a FIEGARCH model for the daily log-returns of the S&P500 U.S. stock market index is provided. [ABSTRACT FROM AUTHOR]

In this paper, we present some computational aspects for a Bayesian analysis involving stable distributions. It is well known that, in general, there is no closed form for the probability density function of a stable distribution. However, the use of a latent or auxiliary random variable facilitates obtaining any posterior distribution when related to stable distributions. To show the usefulness of the computational aspects, the methodology is applied to linear and non-linear regression models. Posterior summaries of interest are obtained using the OpenBUGS software. [ABSTRACT FROM AUTHOR]

In this work we analyze the convergence in distribution sense of the periodogram function (to the spectral density function) based on a time series of a stationary process X[sub t] = (ψ º T[sup t])(X[sub 0]) obtained from the iterations of a continuous transformation T invariant for an ergodic probability μ and a continuous function ψ taking values in R. We only assume a certain rate of convergence to zero for the autocovariance coefficient of the stochastic process, i.e. we assume there exist C > 0 and β > 2 such that γx(h) ≤ Ch+[sup -β], for all h ∈ N, where γx(h) = ∞(ψ º T[sup h])(x)ψ(x)dµ(x) - (∞ ψ(x)dµ(X))² is the h-autocovariance of the process. Our result applies to the case of exponential decay of correlation (or covariance), as it happens for a continuous expanding transformation T on the circle and a Holder potential ψ. It can also be applied to the case when the transformation T has a fixed point with derivative equal to one. [ABSTRACT FROM AUTHOR]

Genetic data are frequently categorical and have complex dependence structures that are not always well understood. For this reason, clustering and classification based on genetic data, while highly relevant, are challenging statistical problems. Here we consider a versatile U-statistics-based approach for non-parametric clustering that allows for an unconventional way of solving these problems. In this paper we propose a statistical test to assess group homogeneity taking into account multiple testing issues and a clustering algorithm based on dissimilarities within and between groups that highly speeds up the homogeneity test. We also propose a test to verify classification significance of a sample in one of two groups. We present Monte Carlo simulations that evaluate size and power of the proposed tests under different scenarios. Finally, the methodology is applied to three different genetic data sets: global human genetic diversity, breast tumour gene expression and Dengue virus serotypes. These applications showcase this statistical framework's ability to answer diverse biological questions in the high dimension low sample size scenario while adapting to the specificities of the different datatypes. [ABSTRACT FROM AUTHOR]