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Quantile-Wavelet Nonparametric Estimates for Time-Varying Coefficient Models. MATHEMATICS 2022. [DOI: 10.3390/math10132321] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/27/2023]
Abstract
The paper considers quantile-wavelet estimation for time-varying coefficients by embedding a wavelet kernel into quantile regression. Our methodology is quite general in the sense that we do not require the unknown time-varying coefficients to be smooth curves of a common degree or the errors to be independently distributed. Quantile-wavelet estimation is robust to outliers or heavy-tailed data. The model is a dynamic time-varying model of nonlinear time series. A strong Bahadur order O2mn3/4(logn)1/2 for the estimation is obtained under mild conditions. As applications, the rate of uniform strong convergence and the asymptotic normality are derived.
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Zhou X, Shen H, Ni B, Xu Y. Wavelet- L1-estimation for non parametric location-scale models under a general dependence framework. COMMUN STAT-THEOR M 2021. [DOI: 10.1080/03610926.2021.1972312] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
Affiliation(s)
- Xingcai Zhou
- School of Economics and Management, Southeast University, Nanjing, China
- School of Statistics and Data Science, Nanjing Audit University, Nanjing, China
| | - Hao Shen
- School of Statistics and Data Science, Nanjing Audit University, Nanjing, China
| | - Beibei Ni
- School of Statistics and Data Science, Nanjing Audit University, Nanjing, China
| | - Yingzhi Xu
- School of Economics and Management, Southeast University, Nanjing, China
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Abstract
The purpose of this note is to introduce and investigate the nonparametric estimation of the conditional mode using wavelet methods. We propose a new linear wavelet estimator for this problem. The estimator is constructed by combining a specific ratio technique and an established wavelet estimation method. We obtain rates of almost sure convergence over compact subsets of Rd. A general estimator beyond the wavelet methodology is also proposed, discussing adaptivity within this statistical framework.
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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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Afshari M, Lak F, Gholizadeh B. A new Bayesian wavelet thresholding estimator of nonparametric regression. J Appl Stat 2016. [DOI: 10.1080/02664763.2016.1182130] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
Affiliation(s)
- M. Afshari
- Department of Statistics, College of Science, Persian Gulf University, Bushehr, Iran
| | - F. Lak
- Department of Statistics, College of Science, Persian Gulf University, Bushehr, Iran
| | - B. Gholizadeh
- Department of Statistics, College of Science, Persian Gulf University, Bushehr, Iran
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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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Nonparametric estimation of the derivatives of a density by the method of wavelet for mixing sequences. Stat Pap (Berl) 2010. [DOI: 10.1007/s00362-010-0328-3] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
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