arXiv subjects

Simone A. Padoan

Publications and source records attributed to Simone A. Padoan.

23 records · Page 2Linked to original sources

arXiv2018

Records for Some Stationary Dependent Sequences

For a zero-mean, unit-variance second-order stationary univariate Gaussian process we derive the probability that a record at the time $n$, say $X_n$, takes place and derive its distribution function. We study the joint distribution of the arrival time process of records and the distribution of the increments between the first and second record, and the third and second record and we compute the expected number of records. We also consider two consecutive and non-consecutive records, one at time $j$ and one at time $n$ and we derive the probability that the joint records $(X_j,X_n)$ occur as well as their distribution function. The probability that the records $X_n$ and $(X_j,X_n)$ take place and the arrival time of the $n$-th record, are independent of the marginal distribution function, provided that it is continuous. These results actually hold for a second-order stationary process with Gaussian copulas. We extend some of these results to the case of a multivariate Gaussian process. Finally, for a strictly stationary process satisfying some mild conditions on the tail behavior of the common marginal distribution function $F$ and the long-range dependence of the extremes of the process, we derive the asymptotic probability that the record $X_n$ occurs and derive its distribution function.

math.ST↗

arXiv2017

Bayesian Inference for the Extremal Dependence

A simple approach for modeling multivariate extremes is to consider the vector of component-wise maxima and their max-stable distributions. The extremal dependence can be inferred by estimating the angular measure or, alternatively, the Pickands dependence function. We propose a nonparametric Bayesian model that allows, in the bivariate case, the simultaneous estimation of both functional representations through the use of polynomials in the Bernstein form. The constraints required to provide a valid extremal dependence are addressed in a straightforward manner, by placing a prior on the coefficients of the Bernstein polynomials which gives probability one to the set of valid functions. The prior is extended to the polynomial degree, making our approach fully nonparametric. Although the analytical expression of the posterior is unknown, inference is possible via a trans-dimensional MCMC scheme. We show the efficiency of the proposed methodology by means of a simulation study. The extremal behaviour of log-returns of daily exchange rates between the Pound Sterling vs the U.S. Dollar and the Pound Sterling vs the Japanese Yen is analysed for illustrative purposes.

stat.ME↗

arXiv2016

Models for extremal dependence derived from skew-symmetric families

Skew-symmetric families of distributions such as the skew-normal and skew-$t$ represent supersets of the normal and $t$ distributions, and they exhibit richer classes of extremal behaviour. By defining a non-stationary skew-normal process, which allows the easy handling of positive definite, non-stationary covariance functions, we derive a new family of max-stable processes - the extremal-skew-$t$ process. This process is a superset of non-stationary processes that include the stationary extremal-$t$ processes. We provide the spectral representation and the resulting angular densities of the extremal-skew-$t$ process, and illustrate its practical implementation (Includes Supporting Information).

stat.ME↗

arXiv2015

Extreme Dependence Models

Extreme values of real phenomena are events that occur with low frequency, but can have a large impact on real life. These are, in many practical problems, high-dimensional by nature (e.g. Tawn, 1990; Coles and Tawn, 1991). To study these events is of fundamental importance. For this purpose, probabilistic models and statistical methods are in high demand. There are several approaches to modelling multivariate extremes as described in Falk et al. (2011), linked to some extent. We describe an approach for deriving multivariate extreme value models and we illustrate the main features of some flexible extremal dependence models. We compare them by showing their utility with a real data application, in particular analyzing the extremal dependence among several pollutants recorded in the city of Leeds, UK.

stat.ME↗

arXiv2009

Likelihood-based inference for max-stable processes

The last decade has seen max-stable processes emerge as a common tool for the statistical modeling of spatial extremes. However, their application is complicated due to the unavailability of the multivariate density function, and so likelihood-based methods remain far from providing a complete and flexible framework for inference. In this article we develop inferentially practical, likelihood-based methods for fitting max-stable processes derived from a composite-likelihood approach. The procedure is sufficiently reliable and versatile to permit the simultaneous modeling of marginal and dependence parameters in the spatial context at a moderate computational cost. The utility of this methodology is examined via simulation, and illustrated by the analysis of U.S. precipitation extremes.

stat.ME↗