TY - JOUR

T1 - On the Riesz estimation of multivariate probability density functions

AU - Reyes, Camilo

AU - Ossandón, Sebastián

AU - Barrientos, Mauricio

N1 - Funding Information:
S. Ossandón acknowledges support from the European Union's Horizon 2020 research and innovation programme under the Marie Sklodowska‐Curie grant agreement No. 777778: MATHROCKS PROJECT and from the project DI INVESTIGACIÓN INNOVADORA INTERDISCIPLINARIA PUCV 2021 No. 039.409/2021. Nanoiónica: Un enfoque interdisciplinario.
Publisher Copyright:
© 2022 John Wiley & Sons, Ltd.

PY - 2022

Y1 - 2022

N2 - In this article, an efficient mathematical procedure is proposed for estimating a multivariate probability density function (mpdf). The method is based on statistical moments but does not require all samples. This is achieved by relating the probability distribution with these statistical moments. The novelty of the method is the calculation of coefficients associated with the mpdf on a suitable Riesz basis chosen for (Formula presented.). The chosen base has several advantages. First, once the coefficients are known to calculate the mpdf, it does not require any matrix inversion. Second, these coefficients can be precalculated and stored. Third, the method is modular, which makes it possible to parallelize the process. These advantages lead us to a very accurate and economical procedure from a cost perspective of computational efforts and time savings. Different numerical examples are presented to prove the effectiveness of our proposed methodology and are compared with more traditional approaches, such as the kernel density method.

AB - In this article, an efficient mathematical procedure is proposed for estimating a multivariate probability density function (mpdf). The method is based on statistical moments but does not require all samples. This is achieved by relating the probability distribution with these statistical moments. The novelty of the method is the calculation of coefficients associated with the mpdf on a suitable Riesz basis chosen for (Formula presented.). The chosen base has several advantages. First, once the coefficients are known to calculate the mpdf, it does not require any matrix inversion. Second, these coefficients can be precalculated and stored. Third, the method is modular, which makes it possible to parallelize the process. These advantages lead us to a very accurate and economical procedure from a cost perspective of computational efforts and time savings. Different numerical examples are presented to prove the effectiveness of our proposed methodology and are compared with more traditional approaches, such as the kernel density method.

KW - coefficients associated with Riesz bases

KW - L(Ω) bases

KW - multivariate probability density function

KW - statistical moments

UR - http://www.scopus.com/inward/record.url?scp=85128515042&partnerID=8YFLogxK

U2 - 10.1002/mma.8302

DO - 10.1002/mma.8302

M3 - Article

AN - SCOPUS:85128515042

JO - Mathematical Methods in the Applied Sciences

JF - Mathematical Methods in the Applied Sciences

SN - 0170-4214

ER -