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de Andrade Lima Neto E, Pinheiro A, Gomes de Oliveira Ferreira A. On wavelet to select the parametric form of a regression model. COMMUN STAT-SIMUL C 2021. [DOI: 10.1080/03610918.2019.1610441] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
Affiliation(s)
| | - Aluísio Pinheiro
- Departamento de Estatística, Universidade Estadual de Campinas, Campinas, SP, Brazil
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Amato U, Antoniadis A, De Feis I, Gijbels I. Penalised robust estimators for sparse and high-dimensional linear models. STAT METHOD APPL-GER 2020. [DOI: 10.1007/s10260-020-00511-z] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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Xiao J, Li X, Shi J. Estimation in a semiparametric partially linear errors-in-variables model with inverse Gaussian kernel. COMMUN STAT-THEOR M 2019. [DOI: 10.1080/03610926.2018.1496255] [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)
- Juxia Xiao
- School of Mathematics and Computer Science, Shanxi Normal University, Linfen, People’s Republic of China
| | - Xu Li
- School of Mathematics and Computer Science, Shanxi Normal University, Linfen, People’s Republic of China
| | - Jianhong Shi
- School of Mathematics and Computer Science, Shanxi Normal University, Linfen, People’s Republic of China
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Reda Abonazel M, Gad AAE. Robust partial residuals estimation in semiparametric partially linear model. COMMUN STAT-SIMUL C 2018. [DOI: 10.1080/03610918.2018.1494279] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
Affiliation(s)
- Mohamed Reda Abonazel
- Department of Applied Statistics and Econometrics, Institute of Statistical Studies and Research, Cairo University, Giza, Egypt
| | - Ahmed Abd-Elfatah Gad
- Department of Statistics and Insurance, Faculty of Commerce, Zagazig University, Zagazig, Egypt
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Zeng Z, Liu X. A difference-based approach in the partially linear model with dependent errors. JOURNAL OF INEQUALITIES AND APPLICATIONS 2018; 2018:267. [PMID: 30363843 PMCID: PMC6182447 DOI: 10.1186/s13660-018-1857-x] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 06/10/2018] [Accepted: 09/18/2018] [Indexed: 06/08/2023]
Abstract
We study asymptotic properties of estimators of parameter and non-parameter in a partially linear model in which errors are dependent. Using a difference-based and ordinary least square (DOLS) method, the estimator of an unknown parametric component is given and the asymptotic normality of the DOLS estimator is obtained. Meanwhile, the estimator of a nonparametric component is derived by the wavelet method, and asymptotic normality and the weak convergence rate of the wavelet estimator are discussed. Finally, the performance of the proposed estimator is evaluated by a simulation study.
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Affiliation(s)
- Zhen Zeng
- Department of Statistics, Jinan University, Guangzhou, P.R. China
| | - Xiangdong Liu
- Department of Statistics, Jinan University, Guangzhou, P.R. China
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Vajpayee V, Mukhopadhyay S, Tiwari AP. Wavelet operator for multiscale modeling of a nuclear reactor. NUCLEAR ENGINEERING AND TECHNOLOGY 2018. [DOI: 10.1016/j.net.2018.02.003] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/17/2022]
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Statistical inference in the partial linear models with the double smoothing local linear regression method. J Stat Plan Inference 2014. [DOI: 10.1016/j.jspi.2013.10.004] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
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Online Semiparametric Identification of Lithium-Ion Batteries Using the Wavelet-Based Partially Linear Battery Model. ENERGIES 2013. [DOI: 10.3390/en6052583] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
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Gannaz I. Wavelet penalized likelihood estimation in generalized functional models. TEST-SPAIN 2013. [DOI: 10.1007/s11749-012-0310-6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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Zhao H, You J. Difference based estimation for partially linear regression models with measurement errors. J MULTIVARIATE ANAL 2011. [DOI: 10.1016/j.jmva.2011.04.009] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
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Abstract
Variable selection is fundamental in high-dimensional statistical modelling, including non-and semiparametric regression. However, little work has been done for variable selection in a partially linear model (PLM). We propose and study a unified approach via double penalized least squares, retaining good features of both variable selection and model estimation in the framework of PLM. The proposed method is distinguished from others in that the penalty functions combine the l1 penalty coming from wavelet thresholding in the non-parametric component with the l1 penalty from the lasso in the parametric component. Simulations are used to investigate the performances of the proposed estimator in various settings, illustrating its effectiveness for simultaneous variable selection as well as estimation.
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Affiliation(s)
- Huijuan Ding
- ORSTAT and Leuven Statistics Research Center, K.U.Leuven, Belgium
| | - Gerda Claeskens
- ORSTAT and Leuven Statistics Research Center, K.U.Leuven, Belgium
| | - Maarten Jansen
- Departments of Mathematics and Computer Science, Università Libre de Bruxelles, Belgium
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Wang L, Brown LD, Cai TT. A difference based approach to the semiparametric partial linear model. Electron J Stat 2011. [DOI: 10.1214/11-ejs621] [Citation(s) in RCA: 33] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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Consistent output estimate with wavelets: An alternative solution of least squares minimization problem for identification of the LZC system of a large PHWR. ANN NUCL ENERGY 2010. [DOI: 10.1016/j.anucene.2010.03.006] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
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Gold D, Mallick B, Coombes K. Real-Time Gene Expression: Statistical Challenges in Design and Inference. J Comput Biol 2008; 15:611-23. [DOI: 10.1089/cmb.2007.0220] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Affiliation(s)
- David Gold
- Department of Mathematics and Statistics, Boston University, Boston, Massachusetts
| | - Bani Mallick
- Department of Statistics, Texas A&M University, College Station, Texas
| | - Kevin Coombes
- Department of Bioinformatics, The University of Texas M.D. Anderson Cancer Center, Houston, Texas
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Afshinpour B, Hossein-Zadeh GA, Soltanian-Zadeh H. Nonparametric trend estimation in the presence of fractal noise: application to fMRI time-series analysis. J Neurosci Methods 2008; 171:340-8. [PMID: 18482771 DOI: 10.1016/j.jneumeth.2008.03.017] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/12/2007] [Revised: 03/26/2008] [Accepted: 03/27/2008] [Indexed: 11/29/2022]
Abstract
Unknown low frequency fluctuations called "trend" are observed in noisy time-series measured for different applications. In some disciplines, they carry primary information while in other fields such as functional magnetic resonance imaging (fMRI) they carry nuisance effects. In all cases, however, it is necessary to estimate them accurately. In this paper, a method for estimating trend in the presence of fractal noise is proposed and applied to fMRI time-series. To this end, a partly linear model (PLM) is fitted to each time-series. The parametric and nonparametric parts of PLM are considered as contributions of hemodynamic response and trend, respectively. Using the whitening property of wavelet transform, the unknown components of the model are estimated in the wavelet domain. The results of the proposed method are compared to those of other parametric trend-removal approaches such as spline and polynomial models. It is shown that the proposed method improves activation detection and decreases variance of the estimated parameters relative to the other methods.
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Affiliation(s)
- Babak Afshinpour
- Control and Intelligent Processing Center of Excellence, Electrical and Computer Engineering Department, Faculty of Engineering, University of Tehran, Tehran, Iran.
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Antoniadis A. Wavelet methods in statistics: some recent developments and their applications. STATISTICS SURVEYS 2007. [DOI: 10.1214/07-ss014] [Citation(s) in RCA: 94] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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