Francois Perron | Université de Montréal (original) (raw)

Uploads

Papers by Francois Perron

Canadian Journal of Statistics, 2008

Any continuous bivariate distribution can be expressed in terms of its margins and a unique copul... more Any continuous bivariate distribution can be expressed in terms of its margins and a unique copula. In the case of extreme-value distributions, the copula is characterized by a dependence function while each margin depends on three parameters. The authors propose a Bayesian approach for the simultaneous estimation of the dependence function and the parameters defining the margins. They describe a nonparametric model for the dependence function and a reversible jump Markov chain Monte Carlo algorithm for the computation of the Bayesian estimator. They show through simulations that their estimator has a smaller mean integrated squared error than classical nonparametric estimators, especially in small samples. They illustrate their approach on a hydrological data set. Un estimateur bayésien de la fonction de dépendance d'une loi des valeurs extrêmes bivariée Résumé : Toute loi bivariée continue peut s'écrire en fonction de ses marges et d'une copule unique. Dans le cas des lois des valeurs extrêmes, la copule est caractérisée par une fonction de dépendance tandis que chaque marge dépend de trois paramètres. Les auteurs proposent une approche bayésienne pour l'estimation simultanée de la fonction de dépendance et des paramètres définissant les marges. Ils décrivent un modèle non paramétrique pour la fonction de dépendance et un algorithme MCMCà sauts réversibles pour le calcul de l'estimateur bayésien. Ils montrent par simulation que l'erreur quadratique moyenne intégrée de leur estimateur est plus faible que celle des estimateurs classiques, surtout dans de petitséchantillons. Ils illustrent leur proposà l'aide de données hydrologiques.

The Annals of Applied Probability, 2004

We build optimal exponential bounds for the probabilities of large deviations of sums n k=1 f (X ... more We build optimal exponential bounds for the probabilities of large deviations of sums n k=1 f (X k) where (X k) is a finite reversible Markov chain and f is an arbitrary bounded function. These bounds depend only on the stationary mean E π f, the end-points of the support of f , the sample size n and the second largest eigenvalue λ of the transition matrix.

In this paper, we propose a new class of discrete time stochastic processes generated by a two-co... more In this paper, we propose a new class of discrete time stochastic processes generated by a two-color generalized Pólya urn, that is reinforced every time. A single urn contains a white balls, b black balls and evolves as follows: at discrete times we sample 1

Statistics & probability letters, 2003

We build optimal exponential bounds for the probabilities of large deviations of sums Sn=∑1nXi of... more We build optimal exponential bounds for the probabilities of large deviations of sums Sn=∑1nXi of independent Bernoulli random variables from their mean nμ. These bounds depend only on the sample size n. Our results improve previous results obtained by Hoeffding and, more recently, by Talagrand. We also prove a global stochastic order dominance for the Binomial law and shows how

A bivariate distribution with continuous margins can be uniquely decomposed via a copula and its ... more A bivariate distribution with continuous margins can be uniquely decomposed via a copula and its marginal distributions. We consider the problem of estimating the copula function and adopt a nonparametric Bayesian approach. On the space of copula functions, we construct a finite dimensional approximation subspace which is parameterized by a doubly stochastic matrix. A major problem here is the selection

The tail of a bivariate distribution function in the domain of attraction of a bivariate extreme-... more The tail of a bivariate distribution function in the domain of attraction of a bivariate extreme-value distribution may be approximated by the one of its extremevalue attractor. The extreme-value attractor has margins that belong to a threeparameter family and a dependence structure which is characterised by a spectral measure, that is a probability measure on the unit interval with mean equal to one half. As an alternative to parametric modelling of the spectral measure, we propose an infinite-dimensional model which is at the same time manageable and still dense within the class of spectral measures. Inference is done in a Bayesian framework, using the censored-likelihood approach. In particular, we construct a prior distribution on the class of spectral measures and develop a trans-dimensional Markov chain Monte Carlo algorithm for numerical computations. The method provides a bivariate predictive density which can be used for predicting the extreme outcomes of the bivariate distribution. In a practical perspective, this is useful for computing rare event probabilities and extreme conditional quantiles. The methodology is validated by simulations and applied to a data-set of Danish fire insurance claims.

We consider the problem of estimating the parameter p of a Binomial(n, p) distribution when p lie... more We consider the problem of estimating the parameter p of a Binomial(n, p) distribution when p lies in the symmetric interval about 1/2 of the form (a, 1 − a), with a ∈ (0, 1/2). For a class of loss functions, which includes the important cases of squared error and information-normalized losses, we investigate conditions for which the Bayes estimator,

Statistics & Risk Modeling, 2000

Let S n = n k=1 X k X k+1 and S = lim n→∞ S n where {X k } ∞ k=1 are independent Bernoulli random... more Let S n = n k=1 X k X k+1 and S = lim n→∞ S n where {X k } ∞ k=1 are independent Bernoulli random variables with mean p k . For the particular case when p k = 1 k+B with B ≥ 0, we show that the distribution of S is a Beta mixture of Poisson distributions. We also give an interesting connection with a matching type problem.

Statistics & Probability Letters, 2002

For estimating under squared-error loss the mean of a p-variate normal distribution when this mea... more For estimating under squared-error loss the mean of a p-variate normal distribution when this mean lies in a ball of radius m centered at the origin and the covariance matrix is equal to the identity matrix, it is shown that the Bayes estimator with respect to a uniformly distributed prior on the boundary of the parameter space (δBU) is minimax

Statistics and Computing, 2008

Different strategies have been proposed to improve mixing and convergence properties of Markov Ch... more Different strategies have been proposed to improve mixing and convergence properties of Markov Chain Monte Carlo algorithms. These are mainly concerned with customizing the proposal density in the Metropolis–Hastings algorithm to the specific target density and require a detailed exploratory analysis of the stationary distribution and/or some preliminary experiments to determine an efficient proposal. Various Metropolis–Hastings algorithms have been suggested

Statistical Papers, 2012

In this paper we study the problem of reducing the bias of the ratio estimator of the population ... more In this paper we study the problem of reducing the bias of the ratio estimator of the population mean in a ranked set sampling (RSS) design. We first propose a jackknifed RSS-ratio estimator and then introduce a class of almost unbiased RSS-ratio estimators of the population mean. We also present an unbiased RSS-ratio estimator of the mean using the idea of Hartley and Ross (Nature 174:270-271, 1954) which performs better than its counterpart with simple random sample data. We show that under certain conditions the proposed unbiased and almost unbiased RSS-ratio estimators perform better than the commonly used (biased) RSS-ratio estimator in estimating the population mean in terms of the mean square error. The theoretical results are augmented by a simulation study using a wheat yield data set from the Iranian Ministry of Agriculture to demonstrate the practical benefits of our proposed ratio-type estimators relative to the RSS-ratio estimator in reducing the bias in estimating the average wheat production.

Journal of Theoretical Probability, 2000

Let {X k } k \ 1 be independent Bernoulli random variables with parameters p k . We study the dis... more Let {X k } k \ 1 be independent Bernoulli random variables with parameters p k . We study the distribution of the number or runs of length 2: that is S n =; n k=1 X k X k+1 . Let S=lim n Q . S n . For the particular case p k =1/(k+B), B being given, we show that the distribution of S is a Beta mixture of Poisson distributions. When B=0 this is a Poisson(1) distribution. For the particular case p k =p for all k we obtain the generating function of S n and the limiting distribution of S n for p=`lh+O(1/`n).