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Chesneau C, Doosti H, Stone L. Adaptive wavelet estimation of a function from an m-dependent process with possibly unbounded m. COMMUN STAT-THEOR M 2019. [DOI: 10.1080/03610926.2018.1423700] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
Affiliation(s)
- Christophe Chesneau
- Laboratoire de Mathématiques Nicolas Oresme, Université de Caen Normandie BP Caen Cedex, France
| | - Hassan Doosti
- Department of Statistics, Macquarie University, Sydney, Australia
| | - Lewi Stone
- Department of Mathematical and Geospatial Sciences, RMIT University, Melbourne, Australia
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Prakasa Rao BLS. Wavelet estimation for derivative of a density in the presence of additive noise. BRAZ J PROBAB STAT 2018. [DOI: 10.1214/17-bjps369] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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Chagny G, Comte F, Roche A. Adaptive estimation of the hazard rate with multiplicative censoring. J Stat Plan Inference 2017. [DOI: 10.1016/j.jspi.2016.11.002] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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Rao BP. Wavelet estimation for derivative of a density in a GARCH-type model. COMMUN STAT-THEOR M 2017. [DOI: 10.1080/03610926.2015.1044671] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
Affiliation(s)
- B.L.S. Prakasa Rao
- CR Rao Advanced Institute of Mathematics, Statistics and Computer Science, Hyderabad, Telengana, India
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Badaoui M, Rhomari N. -Almost sure convergence for multivariate probability density estimate from dependent observations. COMMUN STAT-THEOR M 2017. [DOI: 10.1080/03610926.2015.1019139] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
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Nonparametric density and survival function estimation in the multiplicative censoring model. TEST-SPAIN 2016. [DOI: 10.1007/s11749-016-0479-1] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
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Belomestny D, Comte F, Genon-Catalot V. Nonparametric Laguerre estimation in the multiplicative censoring model. Electron J Stat 2016. [DOI: 10.1214/16-ejs1203] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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A General Result on the Mean Integrated Squared Error of the Hard Thresholding Wavelet Estimator under α-Mixing Dependence. JOURNAL OF PROBABILITY AND STATISTICS 2014. [DOI: 10.1155/2014/403764] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022] Open
Abstract
We consider the estimation of an unknown functionffor weakly dependent data (α-mixing) in a general setting. Our contribution is theoretical: we prove that a hard thresholding wavelet estimator attains a sharp rate of convergence under the mean integrated squared error (MISE) over Besov balls without imposing too restrictive assumptions on the model. Applications are given for two types of inverse problems: the deconvolution density estimation and the density estimation in a GARCH-type model, both improve existing results in this dependent context. Another application concerns the regression model with random design.
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