Publication:
Nonparametric estimation of cumulative distribution function from noisy data in the presence of Berkson and classical errors
Nonparametric estimation of cumulative distribution function from noisy data in the presence of Berkson and classical errors
| datacite.subject.fos | oecd::Natural sciences::Computer and information sciences | |
| dc.contributor.author | Cao Xuan Phuong | |
| dc.contributor.author | Le Thi Hong Thuy | |
| dc.contributor.author | Vo Nguyen Tuyet Doan | |
| dc.date.accessioned | 2022-10-31T08:04:47Z | |
| dc.date.available | 2022-10-31T08:04:47Z | |
| dc.date.issued | 2021 | |
| dc.description.abstract | Let X, Y ,W, δ and ε be continuous univariate random variables defined on a probability space such that Y = X + ε and W = X + δ. Herein X, δ and ε are assumed to be mutually independent. The variables ε and δ are called classical and Berkson errors, respectively. Their distributions are known exactly. Supposewe only observe a random sample Y1, . . . , Yn from the distribution of Y . This paper is devoted to a nonparametric estimation of the unknown cumulative distribution function FW of W based on the observations as well as on the distributions of ε, δ. An estimator for FW depending on a smoothing parameter is suggested. It is shown to be consistent with respect to the mean squared error. Under certain regularity assumptions on the densities of X, δ and ε, we establish some upper and lower bounds on the convergence rate of the proposed estimator. Finally, we perform some numerical examples to illustrate our theoretical results. | |
| dc.identifier.doi | 10.1007/s00184-021-00830-5 | |
| dc.identifier.uri | http://repository.vlu.edu.vn:443/handle/123456789/420 | |
| dc.language.iso | en_US | |
| dc.relation.ispartof | Metrika | |
| dc.relation.issn | 0026-1335 | |
| dc.relation.issn | 1435-926X | |
| dc.subject | "Cumulative distribution function | |
| dc.subject | Deconvolution | |
| dc.subject | Berkson errors | |
| dc.subject | Classical errors" | |
| dc.title | Nonparametric estimation of cumulative distribution function from noisy data in the presence of Berkson and classical errors | |
| dc.type | journal-article | |
| dspace.entity.type | Publication | |
| oaire.citation.issue | 3 | |
| oaire.citation.volume | 85 |
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