In simulation study derived method is compared with no measurement error case.
📌 3 Key Takeaways
🎯
Objective & Hypothesis:Most of the work on wavelet estimation when the variables are measured with errors have centered around nonparametric approaches which cause curse of dimensionality.
📊
Key Findings & Data:In this paper it is aimed to avoid this complexity using wavelet semiparametric errors in variables regression model.
💡
Conclusion & Impact:In simulation study derived method is compared with no measurement error case.
🔬Design:Modeling & Simulation
📍Scope:Comprehensive Sample
⚙️Variables:Partially linear models · semiparametric models · errors in variables
Abstract
Most of the work on wavelet estimation when the variables are measured with errors have centered around nonparametric approaches which cause curse of dimensionality. In this paper it is aimed to avoid this complexity using wavelet semiparametric errors in variables regression model. Using theoretical arguments for nonparametric wavelet estimation a wavelet approach is represented to estimate partially linear errors in variables model which is a semiparametric model when explanatory variable of nonparametric part has measurement error. Assuming that the measurement error has a known distribution we derive an estimator of the linear parts' parameter. In simulation study derived method is compared with no measurement error case.
YALAZ, S. (2019). Wavelet estimation of semiparametric errors in variables model. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, Cilt: 68 - Sayı: 1, 595–601. https://ajindex.com/articles/747073
Qiu, P., Image Processing and Jump Regression Analysis, Wiley, New York, 2005.
Takeda, H., Farsiu, S. and Milanfar, P., Kernel regression for image processing and reconstruction, IEEE Trans. Image Process 16(2) (2007), 349--366. Moura, J.M.F., What is signal processing?, President's Message, IEEE Signal Processing Magazine 26(6) (2009), 6. Rioul, O. and Vetterli, M., Wavelets and signal processing, IEEE Signal Processing Magazine 8 (1991), 14--38. Chang, X. and Qu, L., Wavelet estimation of partially linear models, Computational Statistics and Data Analysis 47(1) (2004), 31--48. Chichignoud, M., Hoang, V.H., Ngoc, T.M.P. and Rivoirard, V., Adaptive wavelet multivariate regression with errors in variables, Electronic Journal of Statistics, 11 (2017), 682--724. Fan, J.and Truong, Y.K., Nonparametric regression with errors in variables, Annals of Statistics, 21 (1993), 1900--1925.
Liang, H., Asymptotic normality of parametric part in partially linear model with measurement error in the non-parametric part, Journa Yalaz: Yalaz, S., Semiparametric regression models with errors in variables, PhD Thesis (2015),
Dicle University, Turkey. Goldenshluger, A. and Lepski, O., Bandwidth selection rule in kernel density estimation: oracle inequalities and adaptive minimax optimality, Ann. Statist. 39(3) (2011), 1608--1632. Hardle, W., Kerkyecharian, G., Picard, D. and Tsybakov, A., Wavelets, approximation, and statistical applications, Volume 129 of Lecture Notes in Statistics, Springer-Verlag, New York, 1998.
Nadaraya, E.A., On nonparametric estimates of density functions and regression curves, Theor. Probability Appl. 10 (1965), 186--190. Watson, G.S., Smooth regression analysis, Sankhya Ser. A 26 (1964), 359--378. Schimek, M.G., Estimation and inference in partially linear models with smoothing splines, Journal of Statistical Planning and Inference 91 (2000), 525--540. Nason, G.P., Wavelet shrinkage using cross-validation, J. Roy. Statist. Soc. Ser. B 58 (1996), 463--479.