Heteroscedastic Deconvolution of P(X<Y) with Compactly Supported Error Densities
We deal with the problem of the nonparametric estimation of P X < Y which is also known as the stress–strength model problem when both X and Y are observed with additional errors. We provide the convergence rate for the suggested estimator and give a lower bound in the case that the error random...
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| Published in | Journal of statistical theory and practice Vol. 13; no. 3 |
|---|---|
| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Cham
Springer International Publishing
01.09.2019
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| Subjects | |
| Online Access | Get full text |
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| Abstract | We deal with the problem of the nonparametric estimation of
P
X
<
Y
which is also known as the stress–strength model problem when both
X
and
Y
are observed with additional errors. We provide the convergence rate for the suggested estimator and give a lower bound in the case that the error random variables have different distributions. Some numerical results are also presented. |
|---|---|
| AbstractList | We deal with the problem of the nonparametric estimation of
P
X
<
Y
which is also known as the stress–strength model problem when both
X
and
Y
are observed with additional errors. We provide the convergence rate for the suggested estimator and give a lower bound in the case that the error random variables have different distributions. Some numerical results are also presented. |
| Author | Lan, Nguyen Nhu Trong, Dang Duc Nguyen, Ton That Quang |
| Author_xml | – sequence: 1 givenname: Dang Duc surname: Trong fullname: Trong, Dang Duc email: ddtrong@hcmus.edu.vn organization: Faculty of Mathematics and Computer Science, University of Science, Ho Chi Minh National University – sequence: 2 givenname: Ton That Quang surname: Nguyen fullname: Nguyen, Ton That Quang organization: Faculty of Mathematics and Computer Science, University of Science, Ho Chi Minh National University, Faculty of Fundamental Science, Industrial University of Ho Chi Minh City – sequence: 3 givenname: Nguyen Nhu surname: Lan fullname: Lan, Nguyen Nhu organization: Faculty of Fundamental Science, Open University |
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| ContentType | Journal Article |
| Copyright | Grace Scientific Publishing 2019 |
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| DOI | 10.1007/s42519-019-0050-y |
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| Keywords | 62G05 Convergence rate Deconvolution 62G99 Heteroscedastic Estimator |
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| References | DelaigleAMeisterADensity estimation with heteroscedastic errorBernoulli200814562579254410210.3150/08-BEJ121 TrongDDNguyenTTQPhuongCXSupplement to “Deconvolution of P(X<Y)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$P(X<Y)$$\end{document} with compactly supported error densities”Stat Probab Lettt201712317117610.1016/j.spl.2016.12.014 CookJRStefanskiLASimulation-extrapolation estimation in parametric measurement error modelsJ Am Stat Assoc1994891314132810.1080/01621459.1994.10476871 KotzSLumelskiiSPenskyMThe stress–strength model and its generalizations theory and applications2003SingaporeWorld Scientific10.1142/5015 DattnerIDeconvolution of PX<Y\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$P\left( X < Y \right)$$\end{document} with supersmooth error distributionsStat Probab Lett20138318801887306989210.1016/j.spl.2013.04.024 KawataTFourier analysis in probability theory1972New YorkAcademic Press0271.60022 Birnbaum ZW (1956) On a use of the Mann–Whitney statistics. In: Proceedings of the 3rd Berkley symposium, vol 1, pp 13–17 HughesGMcRobertsNBurnettFJDecision-making and diagnosis in diseases managementPlant Pathol19994814715310.1046/j.1365-3059.1999.00327.x CoffinMSukhatmeSReceiver operating characteristic studies and measurement errorsBiometrics19975382383710.2307/2533545 TrongDDNguyenTTQPhuongCXDeconvolution of P(X<Y)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$P(X<Y)$$\end{document} with compactly supported error densitiesStat Probab Lett2017123171176359863510.1016/j.spl.2016.12.014 MetzCEBasic principles of ROC analysisNuclear Med19788283298 DewdneyMMBiggsARTurechekWWA statistical comparison of the reliability of the blossom blight forecasts of MARYBLYT and Cougarblight with receiver operating characteristic (ROC) curve analysisPhytopathology2007971164117610.1094/PHYTO-97-9-1164 KimJGleserLJSIMEX approaches to measurement error in ROC studiesCommun Stat Theory Methods20002924732491180285410.1080/03610920008832617 PepeMThe statistical evaluation of medical tests for classification and prediction2003OxfordOxford University Press1039.62105 HuangKMiJWangZInference about reliability parameter with gamma strength and stressJ Stat Plan Inference2012142848854286387210.1016/j.jspi.2011.10.005 GogoiJBorahMEstimation of reliability for multicomponent systems using exponential Gamma and Lindley stress–strength distributionsJ Reliab Stat Stud2012533411247.90118 HussianMAEssamAAEstimation of R=P[Y<X]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R=P[Y < X]$$\end{document} for the inverted exponential distributionInt J Math Arch2013417 |
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| Snippet | We deal with the problem of the nonparametric estimation of
P
X
<
Y
which is also known as the stress–strength model problem when both
X
and
Y
are observed... |
| SourceID | springer |
| SourceType | Publisher |
| SubjectTerms | Mathematics and Statistics Original Article Probability Theory and Stochastic Processes Statistical Theory and Methods Statistics |
| Title | Heteroscedastic Deconvolution of P(X<Y) with Compactly Supported Error Densities |
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