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Harouna Sangaré

Publications and source records attributed to Harouna Sangaré.

8 recordsLinked to original sources
arXiv2026

A Comparative Evaluation of Sample Selection Algorithms for Multivariate Calibration in Near-Infrared Spectroscopic Analysis of Pharmaceutical Formulations

The construction of robust multivariate calibration models for near-infrared (NIR) spectroscopic analysis necessitates careful partitioning of samples into training and validation sets. The selection strategy employed fundamentally influences model generalizability and predictive accuracy. This investigation presents a systematic comparative analysis of four established sample selection algorithms-Duplex, Honigs, Kennard-Stone, and Naes-applied to NIR spectral data acquired from 58 commercial paracetamol tablets. Gaussian process regression (GPR) served as the modeling framework, with model performance quantified through the coefficient of determination (R^2) and root mean square error of prediction (RMSEP). The Kennard-Stone algorithm employing the Mahalanobis distance metric demonstrated superior performance, yielding optimal validation statistics (\(R^2 = 0.99999\), RMSEP = \(1.74 \times 10^{-6}\)). Rigorous non-parametric statistical analysis employing Kruskal-Wallis and post-hoc Mann-Whitney U tests with Bonferroni correction confirmed significant performance differences among algorithms (p < 0.001), while revealing statistical equivalence between Kennard-Stone and Honigs methods. Systematic investigation of training set proportions (60-90%) elucidated the monotonic relationship between calibration set size and predictive accuracy. These findings provide evidence-based guidance for optimizing sample selection protocols in pharmaceutical NIR applications and underscore the critical importance of chemometric validation in spectroscopic method development.

physics.optics↗
arXiv2025

On the Glivenko-Cantelli theorem for real-valued empirical functions of stationary $α$-mixing and $β$-mixing sequences

In this paper we extend the classical Glivenko-Cantelli theorem to real-valued empirical functions under dependence structures characterised by $α$-mixing and $β$-mixing conditions. We investigate sufficient conditions ensuring that families of real-valued functions exhibit the Glivenko-Cantelli (GC) property in these dependence settings. Our analysis focuses on function classes satisfying uniform entropy conditions and establishes deviation bounds under mixing coefficients that decay at appropriate rates. Our results refine the existing literature by relaxing the independence assumptions and highlighting the role of dependence in empirical process convergence.

math.ST↗
arXiv2022

$\mathbf{G}$-Central limit theorems and $\mathbf{G}$-invariance principles for associated random variables

The investigation asymptotic limits on associated data mainly focused on limit theorems of summands of associated data and on the related invariance principles. In a series of papers, we are going to set the general frame of the theory by considering an arbitrary infinitely decomposable (divisible) limit law for summands and study the associated functional laws converging to Lévy processes. The asymptotic frame of Newman (1980) is still used as a main tool. Detailed results are given when $G$ is a Gaussian law (as confirmation of known results) and when $G$ is a Poisson law. In the later case, classical results for independent and identically distributed data are extended to stationary and non-stationary associated data.

math.PR↗
arXiv2022

Extensions of two classical Poisson limit laws to non-stationary independent data

In earlier stages in the introduction to asymptotic methods in probability theory, the weak convergence of sequences $(X_n)_{n\geq 1}$ of Binomial of random variables (\textit{rv}'s) to a Poisson law is classical and easy-to prove. A version of such a result concerning sequences $(Y_n)_{n\geq 1}$ of negative binomial \textit{rv}'s also exists. In both cases, $X_n$ and $Y_n-n$ are by-row sums $S_n[X]$ and $S_n[Y]$ of arrays of Bernoulli \textit{rv}'s and corrected geometric \textit{rv}'s respectively. When considered in the general frame of asymptotic theorems of by-row sums of \textit{rv}'s of arrays, these two simple results in the independent and identically distributed scheme can be generalized to non-stationary data and beyond to non-stationary and dependent data. Further generalizations give interesting results that would not be found by direct methods. In this paper, we focus on generalizations to the non-stationary independent data. Extensions to dependent data will addressed later.

math.PR↗
arXiv2020

Arbitrary functional Glivenko-Cantelli classes and applications to different types of dependence

Using a general strong law of large number proved by Sangaré and Lo (2015) and the entropy numbers, we provide functional Glivenko-Cantelli (GC) classes for arbitrary stationary real-valued random variables (rrv's). Next, the general results are particularized for different types of dependence (association, $ϕ$-mixing, in particular) and compared with available results in the literature.

math.ST↗
arXiv2019

Finiteness of Record values and Alternative Asymptotic Theory of Records with Atom Endpoints

Asymptotic theories on record values and times, including central limit theorems, make sense only if the sequence of records values (and of record times) is infinite. If not, such theories could not even be an option. In this paper, we give necessary and/or sufficient conditions for the finiteness of the number of records. We prove, for example for \textsl{iid} real valued random variable, that strong upper record values are finite if and only if the upper endpoint is finite and is an atom of the common cumulative distribution function. The only asymptotic study left to us concerns the infinite sequence of hitting times of that upper endpoints, which by the way, is the sequence of weak record times. The asymptotic characterizations are made using negative binomial random variables and the dimensional multinomial random variables. Asymptotic comparison in terms of consistency bounds and confidence intervals on the different sequences of hitting times are provide. The example of a binomial random variable is given

math.PR↗
arXiv2016

General Central Limit Theorems for Associated Sequences

In this paper, we provide general central limit theorems (CLT's) for associated random variables (rv's) following the approaches used by Newman (1980) and Olivera et al.(2012). Given some assumptions, a Lyapounov-Feller-Levy type theorem is stated. We next specify different particular CLT versions of associated sequences based on moment conditions. A comparison study with available CTL's is performed. As a by-product, we complete an important available theorem where an assumption was missing.

math.PR↗