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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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Haddad S, Belaide K. Local asymptotic normality for long-memory process with strong mixing noises. COMMUN STAT-THEOR M 2020. [DOI: 10.1080/03610926.2019.1584306] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
Affiliation(s)
- Soraya Haddad
- Department of Mathematics, Applied Mathematics Laboratory, University of Bejaia, Bejaia, Algeria
| | - Karima Belaide
- Applied Mathematics Laboratory, University of Bejaia, Bejaia, Algeria
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Krebs JTN. Non-parametric regression for spatially dependent data with wavelets. STATISTICS-ABINGDON 2018. [DOI: 10.1080/02331888.2018.1506924] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/28/2022]
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Nonparametric regression on random fields with random design using wavelet method. STATISTICAL INFERENCE FOR STOCHASTIC PROCESSES 2015. [DOI: 10.1007/s11203-015-9119-8] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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