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Wavelet shrinkage in estimation of regression function with error in variables | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقالات آماده انتشار، اصلاح شده برای چاپ، انتشار آنلاین از تاریخ 07 اسفند 1403 اصل مقاله (512.78 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2024.34558.5164 | ||
| نویسندگان | ||
| Ghodratollah Rahmati* 1؛ Esmaeil Shirazi2؛ Masoud Yarmohammadi1؛ Parviz Nasiri3 | ||
| 1Department of Statistics, Faculty of Science, Payame Noor University, Tehran, Iran | ||
| 2Department of Statistics, Faculty of Science, Gonbad Kavous University, Gonbad Kavous, Iran | ||
| 3Department of Statistics, Faculty of Science, Payame Noor University, Tehran, Iran | ||
| تاریخ دریافت: 04 تیر 1403، تاریخ پذیرش: 28 شهریور 1403 | ||
| چکیده | ||
| The purpose of this study was to estimate the unknown regression function $h$ in a regression model having errors-in-variables: $(Y,X)$, where $Y=h(U)+E$ and $X=U+T$. We propose a new adaptive estimator through the wavelet shrinkage method to estimate $h$. In particular, the block thresholding method has been investigated by considering some simple assumptions on $E$. Finally, using a simulation study, we have compared the proposed estimator with other threshold estimators. | ||
| کلیدواژه‌ها | ||
| Block Thresholding Method؛ Error in Variable؛ Nonparametric Regression؛ Shrinkage Method؛ Wavelets | ||
| مراجع | ||
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[1] T. Cai, Adaptive wavelet estimation: A block thresholding and Oracle inequality approach, Ann. Statist. 27 (1999), 898–924. [2] C. Chesneau, On adaptive wavelet estimation of the regression function and its derivatives in errors-in-variables model, Theory Appl. 4 (2010), 185–208. [3] C. Chesneau, On Wavelet Block Thresholding in Nonparametric Estimation, Preprint’Laboratoire de Probabilit´es et Modeles Al´eatoires’ Paris VI, 2006. [4] M. Chichignoud and V. Ha Hoong, Adaptive wavelet multivariate regression with errors in variables, Electronic J. Statist. 11 (2017), 682–724. [5] F. Comte and M-L. Taupin, Nonparametric estimation of the regression function in an errors-in-variables model, Statist. Sinica 173 (2007), 1065–1090. [6] J. Fan and M. Marsy, Multivariate regression estimation with errors-in-variables: Asymptotic normality for mixin process, Multivar. Anal. 43 (1992), 237–272. [7] J. Fan, Y.K. Truong, and Y. Wang, Nonparametric function estimation involving errors-in-variables, Roussas, G. (eds) Nonparametric Functional Estimation and Related Topics. NATO ASI Series, vol 335. Springer, 1991, pp. 613–627. [8] J.Y. Koo and K.W. Lee, B-splines estimation of regression function with errors in variables, Statist, Probab. Lett. 40 (1998), 57–66. [9] P. Hall, S. Penev, and J. Tran, Wavelet methods for erratic regression means in the presence of measurement error, Statist. Sinica 28 (2018), no. 4, 2289–2307. [10] D.A. Loannides and P.D. Alevizos, Nonparametric regression with errors-in-variables and application, Statist. Probab. Lett. 32 (1997), 35–43. [11] E. Masry, Multivariate regression estimation with errors-in-variables for stationary processes, Nonparametr. Stattist. 3 (1993), 13–36. [12] J. Shi, X. Bai, and W. Song, Partial deconvolution estimation in nonparametric regression, Canad. J. Statist. 7 (2010), 48–62. | ||
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