Frédéric Ouimet
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View article: ksm: Kernel Density Estimation for Random Symmetric Positive Definite Matrices
ksm: Kernel Density Estimation for Random Symmetric Positive Definite Matrices Open
View article: A Bernstein polynomial approach for the estimation of cumulative distribution functions in the presence of missing data
A Bernstein polynomial approach for the estimation of cumulative distribution functions in the presence of missing data Open
We study nonparametric estimation of univariate cumulative distribution functions (CDFs) pertaining to data missing at random. The proposed estimators smooth the inverse probability weighted (IPW) empirical CDF with the Bernstein operator,…
View article: An omnibus goodness-of-fit test based on trigonometric moments
An omnibus goodness-of-fit test based on trigonometric moments Open
We present a versatile omnibus goodness-of-fit test based on the first two trigonometric moments of probability-integral-transformed data, which rectifies the covariance scaling errors made by Langholz and Kronmal [J. Amer. Statist. Assoc.…
View article: Dirichlet kernel density estimation for strongly mixing sequences on the simplex
Dirichlet kernel density estimation for strongly mixing sequences on the simplex Open
This paper investigates the theoretical properties of Dirichlet kernel density estimators for compositional data supported on simplices, for the first time addressing scenarios involving time-dependent observations characterized by strong …
View article: Results related to the Gaussian product inequality conjecture for mixed-sign exponents in arbitrary dimension
Results related to the Gaussian product inequality conjecture for mixed-sign exponents in arbitrary dimension Open
This note establishes that the opposite Gaussian product inequality (GPI) of the type proved by Russell & Sun (2022a) in two dimensions, and partially extended to higher dimensions by Zhou et al. (2024), continues to hold for an arbitrary …
View article: Local linear smoothing for regression surfaces on the simplex using Dirichlet kernels
Local linear smoothing for regression surfaces on the simplex using Dirichlet kernels Open
This paper introduces a local linear smoother for regression surfaces on the simplex. The estimator solves a least-squares regression problem weighted by a locally adaptive Dirichlet kernel, ensuring good boundary properties. Asymptotic re…
View article: A new adaptive local polynomial density estimation procedure on complicated domains
A new adaptive local polynomial density estimation procedure on complicated domains Open
35 pages, 4 figures
View article: On noncentral Wishart mixtures of noncentral Wisharts and their use for testing random effects in factorial design models
On noncentral Wishart mixtures of noncentral Wisharts and their use for testing random effects in factorial design models Open
It is shown that a noncentral Wishart mixture of noncentral Wishart distributions with the same degrees of freedom yields a noncentral Wishart distribution, thereby extending the main result of Jones and Marchand [Stat 10 (2021), Paper No.…
View article: A comparison of Dirichlet kernel regression methods on the simplex
A comparison of Dirichlet kernel regression methods on the simplex Open
An asymmetric Dirichlet kernel version of the Gasser-Müller estimator is introduced for regression surfaces on the simplex, extending the univariate analog proposed by Chen [Statist. Sinica, 10(1) (2000), pp. 73-91]. Its asymptotic propert…
View article: Normal approximations for the multivariate inverse Gaussian distribution and asymmetric kernel smoothing on d-dimensional half-spaces
Normal approximations for the multivariate inverse Gaussian distribution and asymmetric kernel smoothing on d-dimensional half-spaces Open
View article: Results Related to the Gaussian Product Inequality Conjecture for Mixed-Sign Exponents in Arbitrary Dimension
Results Related to the Gaussian Product Inequality Conjecture for Mixed-Sign Exponents in Arbitrary Dimension Open
View article: A linear regression model for quantile function data applied to paired pulmonary 3d CT scans
A linear regression model for quantile function data applied to paired pulmonary 3d CT scans Open
This paper introduces a new objective measure for assessing treatment response in asthmatic patients using computed tomography (CT) imaging data. For each patient, CT scans were obtained before and after one year of monoclonal antibody tre…
View article: Asymptotics for non-degenerate multivariate <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si2.svg" display="inline" id="d1e336"> <mml:mi>U</mml:mi> </mml:math> -statistics with estimated nuisance parameters under the null and local alternative hypotheses
Asymptotics for non-degenerate multivariate -statistics with estimated nuisance parameters under the null and local alternative hypotheses Open
View article: An explicit Wishart moment formula for the product of two disjoint principal minors
An explicit Wishart moment formula for the product of two disjoint principal minors Open
This paper provides the first explicit formula for the expectation of the product of two disjoint principal minors of a Wishart random matrix, solving a part of a broader problem put forth by Samuel S. Wilks [Ann. of Math. (2) 35 (1934), p…
View article: An explicit Wishart moment formula for the product of two disjoint principal minors
An explicit Wishart moment formula for the product of two disjoint principal minors Open
This paper provides the first explicit formula for the expectation of the product of two disjoint principal minors of a Wishart random matrix, solving a part of a broader problem put forth by Samuel S. Wilks in 1934 in the Annals of Mathem…
View article: Local linear smoothing for regression surfaces on the simplex using Dirichlet kernels
Local linear smoothing for regression surfaces on the simplex using Dirichlet kernels Open
This paper introduces a local linear smoother for regression surfaces on the simplex. The estimator solves a least-squares regression problem weighted by a locally adaptive Dirichlet kernel, ensuring good boundary properties. Asymptotic re…
View article: Integral representations for the joint survival functions of the cumulated components of multinomial random vectors
Integral representations for the joint survival functions of the cumulated components of multinomial random vectors Open
This paper presents a multivariate normal integral expression for the joint survival function of the cumulated components of any multinomial random vector. This result can be viewed as a multivariate analog of Equation (7) from Carter & Po…
View article: On Wilks' joint moment formulas for embedded principal minors of Wishart random matrices
On Wilks' joint moment formulas for embedded principal minors of Wishart random matrices Open
In 1934, the American statistician Samuel S. Wilks derived remarkable formulas for the joint moments of embedded principal minors of sample covariance matrices in multivariate Gaussian populations, and he used them to compute the moments o…
View article: Central and noncentral moments of the multivariate hypergeometric distribution
Central and noncentral moments of the multivariate hypergeometric distribution Open
In this short note, explicit formulas are developed for the central and noncentral moments of the multivariate hypergeometric distribution. A numerical implementation is provided in Mathematica for fast evaluations. This work complements t…
View article: Asymptotics for non-degenerate multivariate $U$-statistics with estimated nuisance parameters under the null and local alternative hypotheses
Asymptotics for non-degenerate multivariate $U$-statistics with estimated nuisance parameters under the null and local alternative hypotheses Open
The large-sample behavior of non-degenerate multivariate $U$-statistics of arbitrary degree is investigated under the assumption that their kernel depends on parameters that can be estimated consistently. Mild regularity conditions are pro…
View article: On the Gaussian product inequality conjecture for disjoint principal minors of Wishart random matrices
On the Gaussian product inequality conjecture for disjoint principal minors of Wishart random matrices Open
View article: A bridge between the circular and linear normal distributions
A bridge between the circular and linear normal distributions Open
In this short note, we present a refined approximation for the log-ratio of the density of the von Mises$(μ,κ)$ distribution (also called the circular normal distribution) to the standard (linear) normal distribution when the concentration…
View article: On the Gaussian product inequality conjecture for disjoint principal minors of Wishart random matrices
On the Gaussian product inequality conjecture for disjoint principal minors of Wishart random matrices Open
This paper extends various results related to the Gaussian product inequality (GPI) conjecture to the setting of disjoint principal minors of Wishart random matrices. This includes product-type inequalities for matrix-variate analogs of co…
View article: Non-asymptotic approximations for Pearson's chi-square statistic and its application to confidence intervals for strictly convex functions of the probability weights of discrete distributions
Non-asymptotic approximations for Pearson's chi-square statistic and its application to confidence intervals for strictly convex functions of the probability weights of discrete distributions Open
In this paper, we develop a non-asymptotic local normal approximation for multinomial probabilities. First, we use it to find non-asymptotic total variation bounds between the measures induced by uniformly jittered multinomials and the mul…
View article: Deficiency bounds for the multivariate inverse hypergeometric distribution
Deficiency bounds for the multivariate inverse hypergeometric distribution Open
The multivariate inverse hypergeometric (MIH) distribution is an extension of the negative multinomial (NM) model that accounts for sampling without replacement in a finite population. Even though most studies on longitudinal count data wi…
View article: Asymptotic comparison of negative multinomial and multivariate normal experiments
Asymptotic comparison of negative multinomial and multivariate normal experiments Open
This note presents a refined local approximation for the logarithm of the ratio between the negative multinomial probability mass function and a multivariate normal density, both having the same mean-covariance structure. This approximatio…
View article: A new adaptive local polynomial density estimation procedure on complicated domains
A new adaptive local polynomial density estimation procedure on complicated domains Open
This paper presents a novel approach for pointwise estimation of multivariate density functions on known domains of arbitrary dimensions using nonparametric local polynomial estimators. Our method is highly flexible, as it applies to both …
View article: Moments of the Negative Multinomial Distribution
Moments of the Negative Multinomial Distribution Open
The negative multinomial distribution appears in many areas of applications such as polarimetric image processing and the analysis of longitudinal count data. In previous studies, general formulas for the falling factorial moments and cumu…
View article: A refined continuity correction for the negative binomial distribution and asymptotics of the median
A refined continuity correction for the negative binomial distribution and asymptotics of the median Open
View article: Minimax properties of Dirichlet kernel density estimators
Minimax properties of Dirichlet kernel density estimators Open
14 pages, 1 figure