François Perron

François Perron
Université de Montréal | UdeM · Department of Mathematics and Statistics

About

46
Publications
1,766
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661
Citations
Citations since 2016
4 Research Items
248 Citations
2016201720182019202020212022010203040
2016201720182019202020212022010203040
2016201720182019202020212022010203040
2016201720182019202020212022010203040

Publications

Publications (46)
Article
A recommender system based on ranks is proposed, where an expert's ranking of a set of objects and a user's ranking of a subset of those objects are combined to make a prediction of the user's ranking of all objects. The rankings are assumed to be induced by latent continuous variables corresponding to the grades assigned by the expert and the user...
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Full-text available
For a normally distributed X ∼ N(μ, σ²) and for estimating μ when restricted to an interval [−m, m] under general loss F (|d − μ|) with strictly increasing and absolutely continuous F, we establish the inadmissibility of the restricted maximum likelihood estimator δmle for a large class of F ’s and provide explicit improvements. In particular, we g...
Article
Distributional results are obtained for runs of length 2 in Bernoulli arrays Xk,j with multinomial distributed rows. These include a multivariate Poisson mixture representation with Dirichlet mixing for the joint distribution of the number of runs in each column.
Article
Pickands dependence functions characterize bivariate extreme value copulas. In this paper, we study the class of polynomial Pickands functions. We provide a solution for the characterization of such polynomials of degree at most $m+2$, $m\geq0$, and show that these can be parameterized by a vector in $\mathbb{R}^{m+1}$ belonging to the intersection...
Article
Full-text available
Distributional findings are obtained relative to various quantities arising in Bernoulli arrays {Xkj,k > 1,j = 1,...,r + 1}, where the rows (Xk,1,...,Xk,r+1) are independently distributed as Multinomial (1,pk, 1,...,pk,r+1) for k > 1 with the homogeneity across the first r columns assumption pk,1 = • • • = pk,r. The quantities of interest relate to...
Article
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 t...
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Full-text available
In this paper, we propose a new class of discrete time stochastic processes generated by a two-color generalized Polya urn, that is reinforced every time. A single urn contains a white balls, b black balls and evolves as follows: at discrete times n=1,2,…, we sample Mn balls and note their colors, say Rn are white and Mn- Rn are black. We return th...
Article
  The tail of a bivariate distribution function in the domain of attraction of a bivariate extreme value distribution may be approximated by that of its extreme value attractor. The extreme value attractor has margins that belong to a three-parameter family and a dependence structure which is characterized by a probability measure on the unit inter...
Article
In the ranked set sampling algorithm a sample of size n 2 is available. The data can be ranked without measurements. A subsample of size n is created using the information given by the ranks. The population mean is estimated by the subsample mean. In this paper, we investigate other ways for creating the subsample. To this end we introduce new samp...
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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...
Article
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 extreme-value attractor. The extreme-value attractor has margins that belong to a three-parameter family and a dependence structure which is characterised by a spectral measure, that is a probabil...
Article
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...
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Full-text available
For the problem of estimating under squared error loss the parameter of a symmetric distribution which is subject to an interval constraint, we develop general theory which provides improvements on various types of inadmissible procedures, such as maximum likelihood procedures. The applications and further developments given include: (i) symmetric...
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Given a Wishart matrix S [S ∽ Wp(n, Σ)] and an independent multinomial vector X [X ∽ Np (μ, Σ)], equivariant estimators of Σ are proposed. These estimators dominate the best multiple of S and the Stein-type truncated estimators.A partir d'une matrice aléatoire S de loi Wishart [S ∽ Wp(n, Σ)] et d'un vecteur aléatoire X de loi multinormale [X ∽ Np(μ...
Article
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 preli...
Article
A crucial problem in Bayesian posterior computation is efficient sampling from a univariate distribution, e.g. a full conditional distribution in applications of the Gibbs sampler. This full conditional distribution is usually non-conjugate, algebraically complex and computationally expensive to evaluate. We propose an alternative algorithm, called...
Article
´For estimating the median θ of a spherically symmetric univariate distribution under squared error loss, when θ is known to be restricted to an interval [−m, m], m known, we derive sufficient conditions for estimators δ to dominate the maximum likelihood estimator δmle. Namely: (i) we identify a large class of models where for sufficiently small m...
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Full-text available
For the problem of estimating under squared error loss the location parameter of a p-variate spherically symmetric distribution where the location parameter lies in a ball of radius m, a general sufficient condition for an estimator to dominate the maximum likelihood estimator is obtained. Dominance results are then made explicit for the case of a...
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This paper proposes methods to improve Monte Carlo estimates when the Independent Metropolis-Hastings Algorithm (IMHA) is used. Our first approach uses a control variate based on the sample generated by the proposal distribution. We derive the variance of our estimator for a fixed sample size n and show that, as n tends to infinity, this variance i...
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Full-text available
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 estimato...
Article
We build optimal exponential bounds for the probabilities of large deviations of sums ∑<sub>k=1</sub><sup>n</sup>f(X<sub>k</sub>) where (X<sub>k</sub>) is a finite reversible Markov chain and f is an arbitrary bounded function. These bounds depend only on the stationary mean ${\mathbb {E}}_{\pi}f,$ the end-points of the support of f, the sample siz...
Article
In this paper we examine the problem of the estimation of the variance σ2 of a population based on a ranked set sample (RSS) from a nonparametric point of view. It is well known that based on a single cycle RSS, there does not exist an unbiased estimate of σ2. We show that for more than one cycle, it is possible to construct a class of quadratic un...
Article
Let {Xk}k ≥ 1 be independent Bernoulli random variables with parameters pk. We study the distribution of the number or runs of length 2: that is Sn = ∑k = 1n Xk Xk+1. Let S = limn → ∞ S n. For the particular case pk = 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(...
Article
We build optimal exponential bounds for the probabilities of large deviations of sums Sn=[summation operator]1n Xi of independent Bernoulli random variables from their mean n[mu]. 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 stochas...
Article
Under a compactness assumption, we show that a φ-irreducible and aperiodic Metropolis-Hastings chain is geometrically ergodic if and only if its rejection probability is bounded away from unity. In the particular case of the independence Metropolis-Hastings algorithm, we obtain that the whole spectrum of the induced operator is contained in (and in...
Article
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 whe...
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Full-text available
We consider the problem of estimating the mean of a $p$-variate normal distribution with identity covariance matrix when the mean lies in a ball of radius $m$. It follows from general theory that dominating estimators of the maximum likelihood estimator always exist when the loss is squared error. We provide and describe explicit classes of improve...
Article
Nonparametric modeling is an indispensable tool in many applications and its formulation in an hierarchical Bayesian context, using the entire posterior distribution rather than particular expectations, increases its flexibility. In this article, the focus is on nonparametric estimation through a mixture of triangular distributions. The optimality...
Article
We propose a new estimator for estimating a quantity μ via Monte Carlo simulations, where μ = ∫ f dP and P is the target probability measure. The new estimator outperforms the usual accept-reject algorithm in terms of reducing the variance. Properties of the estimator are derived. A new Rao-Blackwellised version of the estimator is also produced, b...
Article
The notion of ranked set sampling (RSS) for estimating the mean of a population and its advantage over the use of a simple random sampling for the same purpose are well known.In this paper we provide a new perspective of RSS via the notion of random selection, and discuss some special features of this improved procedure.
Article
We consider the problem of estimating the precision matrix ([Sigma]-1) under a fully invariant convex loss. Suppose that there exists a minimax constant risk estimator[Phi](say) for this problem. K. Krishnamoorthy and A. K. Gupta have proposed an operation which transforms this estimator into an orthogonally invariant estimator[Phi]* (say) and they...
Article
We consider the problem of estimating a p-dimensional vector [mu]1 based on independent variables X1, X2, and U, where X1 is Np([mu]1, [sigma]2[Sigma]1), X2 is Np([mu]2, [sigma]2[Sigma]2), and U is [sigma]2[chi]2n ([Sigma]1 and [Sigma]2 are known). A family of minimax estimators is proposed. Some of these estimators can be obtained via Bayesian arg...
Article
Let S : 2 × 2 have a nonsingular Wishart distribution with unknown matrix σ and n degrees of freedom. For estimating σ two families of mimmax estimators, with respect to the entropy loss, are presented. These estimators are of the form σ(S) = Rø(L)Rt where R is orthogonal, L and Φ are diagonal, and RLRT = S. Conditions under which the components of...
Article
Let S: p × p have a nonsingular Wishart distribution with unknown matrix Σ and n degrees of freedom, n ≥ p. For estimating Σ, a family of minimax estimators, with respect to the entropy loss, is presented. These estimators are of the form (S) = RΦ(L) Rt, where R is orthogonal, L and Φ are diagonal, and RLRt = S. Conditions under which the component...
Article
For the problem of estimating the mean of a p‐dimensional normal distribution, p > 1, confidence regions based on half‐spaces bounded by a hyperplane having the vector of observations as normal are proposed. Confidence regions with exact probability of coverage are constructed. Tables are provided.
Article
Let X1, ..., Xn (n > p > 2) be independently and identically distributed p-dimensional normal random vectors with mean vector [mu] and positive definite covariance matrix [Sigma] and let [Sigma] and . be partioned as1 p-1 1 p-1. We derive here the best equivariant estimators of the regression coefficient vector [beta] = [Sigma]22-1[Sigma]21 and the...
Article
For the problem of estimating the mean of a p-dimensional normal distribution, $p > 1$ , confidence regions based on half-spaces bounded by a hyperplane having the vector of observations as normal are proposed. Confidence regions with exact probability of coverage are constructed. Tables are provided.
Article
Let X = (Xj : j = 1,…, n) be n row vectors of dimension p independently and identically distributed multinomial. For each j, Xj is partitioned as Xj = (Xj1, Xj2, Xj3), where pi is the dimension of Xji with p1 = 1,p1+p2+p3 = p. In addition, consider vectors Yji, i = 1,2j = 1,…,ni that are independent and distributed as X1i. We treat here the problem...
Article
Let X1,...,Xn (n>1, p>1) be independently and identically distributed normal p-vectors with mean [mu] and covariance matrix ([mu]'[mu]/C2)I, where the coefficient of variation C is known. The authors have obtained the best equivariant estimator of [mu] under the loss function L([mu]d)=([mu]-d)'([mu]-d/[mu]'[mu]) They have compared the best equivari...
Article
This paper considers the problems of estimating a mean vector μ under constraint μ′Σ−1μ = 1 or and derives the best equivariant estimators under the loss (a − μ)′ Σ−1(a − μ), which dominate the MLE's uniformly. The results are regarded as multivariate extensions of those with known coefficient of variation in a univariate case. As a particular case...
Article
This paper considers the problems of estimating a mean vector [mu] under constraint [mu]'[Sigma]-1[mu] = 1 or [Sigma]-1/2[mu] = c and derives the best equivariant estimators under the loss (a - [mu])' [Sigma]-1(a - [mu]), which dominate the MLE's uniformly. The results are regarded as multivariate extensions of those with known coefficient of varia...

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