ORCID Profile
0000-0001-7933-5265
Current Organisation
Université du Québec à Montréal
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Publisher: MDPI AG
Date: 16-10-2021
DOI: 10.3390/MATH9202605
Abstract: In this paper, we complement a study recently conducted in a paper of H.A. Mombeni, B. Masouri and M.R. Akhoond by introducing five new asymmetric kernel c.d.f. estimators on the half-line [0,∞), namely the Gamma, inverse Gamma, LogNormal, inverse Gaussian and reciprocal inverse Gaussian kernel c.d.f. estimators. For these five new estimators, we prove the asymptotic normality and we find asymptotic expressions for the following quantities: bias, variance, mean squared error and mean integrated squared error. A numerical study then compares the performance of the five new c.d.f. estimators against traditional methods and the Birnbaum–Saunders and Weibull kernel c.d.f. estimators from Mombeni, Masouri and Akhoond. By using the same experimental design, we show that the LogNormal and Birnbaum–Saunders kernel c.d.f. estimators perform the best overall, while the other asymmetric kernel estimators are sometimes better but always at least competitive against the boundary kernel method from C. Tenreiro.
Publisher: Walter de Gruyter GmbH
Date: 2021
Abstract: We present a general methodology to construct triplewise independent sequences of random variables having a common but arbitrary marginal distribution F (satisfying very mild conditions). For two specific sequences, we obtain in closed form the asymptotic distribution of the s le mean. It is non-Gaussian (and depends on the specific choice of F ). This allows us to illustrate the extent of the ‘failure’ of the classical central limit theorem (CLT) under triplewise independence. Our methodology is simple and can also be used to create, for any integer K , new K -tuplewise independent sequences that are not mutually independent. For K [four.tf], it appears that the sequences created using our methodology do verify a CLT, and we explain heuristically why this is the case.
Publisher: Elsevier BV
Date: 11-2018
Publisher: Informa UK Limited
Date: 25-07-2022
Publisher: Informa UK Limited
Date: 24-11-2022
Publisher: Elsevier BV
Date: 07-2021
Location: United States of America
No related grants have been discovered for Frederic Ouimet.