Publication:
Distribution Estimation of a Sum Random Variable from Noisy Samples
Distribution Estimation of a Sum Random Variable from Noisy Samples
| datacite.subject.fos | oecd::Natural sciences::Mathematics | |
| dc.contributor.author | Cao Xuan Phuong | |
| dc.contributor.author | Le Thi Hong Thuy | |
| dc.date.accessioned | 2022-11-09T09:16:24Z | |
| dc.date.available | 2022-11-09T09:16:24Z | |
| dc.date.issued | 2021 | |
| dc.description.abstract | Let X, Y be independent continuous univariate random variables with unknown distributions. Suppose we observe two independent random samples X′1,…,X′n and Y′1,…,Y′m from the distributions of X′=X+ζ and Y′=Y+η, respectively. Here ζ, η are random noises and have known distributions. This paper is devoted to an estimation for unknown cumulative distribution function (cdf) FX+Y of the sum X+Y on the basis of the samples. We suggest a nonparametric estimator of FX+Y and demonstrate its consistency with respect to the root mean squared error. Some upper and minimax lower bounds on convergence rate are derived when the cdf’s of X, Y belong to Sobolev classes and when the noises are Fourier-oscillating, supersmooth and ordinary smooth, respectively. Particularly, if the cdf’s of X, Y have the same smoothness degrees and n=m, our estimator is minimax optimal in order when the noises are Fourier-oscillating as well as supersmooth. A numerical example is also given to illustrate our method. | |
| dc.identifier.doi | 10.1007/s40840-021-01088-w | |
| dc.identifier.uri | http://repository.vlu.edu.vn:443/handle/123456789/1094 | |
| dc.language.iso | en_US | |
| dc.relation.ispartof | Bulletin of the Malaysian Mathematical Sciences Society | |
| dc.relation.issn | 0126-6705 | |
| dc.relation.issn | 2180-4206 | |
| dc.title | Distribution Estimation of a Sum Random Variable from Noisy Samples | |
| dc.type | journal-article | |
| dspace.entity.type | Publication | |
| oaire.citation.issue | 5 | |
| oaire.citation.volume | 44 |