Using the wavelet analysis to estimate the nonparametric regression model in the presence of associated errors

Document Type : Research Paper


1 Ministry of Interior, Directorate of Human Recourses, Iraq

2 Department of Statistics, College of Administration and Economics University of Baghdad, Baghdad, Iraq


The wavelet shrink estimator is an attractive technique when estimating the nonparametric regression functions, but it is very sensitive in the case of a correlation in errors. In this research, a polynomial model of low degree was used for the purpose of addressing the boundary problem in the wavelet reduction in addition to using flexible threshold values in the case of Correlation in errors as it deals with those transactions at each level separately, unlike the comprehensive threshold values that deal with all levels simultaneously, as (Visushrink) methods, (False Discovery Rate) method, (Improvement Thresholding) and (Sureshrink method), as the study was conducted on real monthly data represented in the rates of theft crimes for juveniles in Iraq, specifically the Baghdad governorate, and the risk ratios about those crimes for the years 2008-2018, with a sample size of (128) (Sureshrink) The study also showed an increase in the rate of theft crimes for juveniles in recent years.


[1] F. Abramovich and Y. Benjamini, Adaptive thresholding of wavelet coefficients, Comput. Stat. Data Anal. 22(4) (1996) 351–361.
[2] L.D. Donoho and M.I. Johnstone, Ideal spatial adaptation by wavelet shrinkage, Biometrika 81(3) (1994) 425–55.
[3] C. He, J. Xing, J. Li, Q. Yang and R. Wang, A New wavelet threshold determination method considering intercalate correlation in signal denoising, Math. Prob. Engin. 2015 (2015) Article ID 280251.
[4] I. Johnstone, Wavelet shrinkage for correlated data and inverse problems: A daptivity results, Stat. Sinica 9 (1999) 51–83.
[5] S.C. Mallat, A Theory for multiresolution signal De composition: The wavelet Representation, IEEE Trans. Pattern Machine Intell. 11(7) (1989).
[6] S. Mupparaju, B. Naga and V.S. Jahuvvi, Comparison of varians thresholding techniques of image denoising, Int. J. Engin. Res. Technol. 2(9) (2013).
[7] G.P. Nason and B.W. Silverman, Wavelet for Regression and Other Statistical Problems, School of Mathematics, University of Bristol, 1997.
[8] P.G. Nason, Choice of The Threshold Parameter in Wavelet Function Estimation, Springer, 1995.
[9] S.H. Oh and M.C.T. Lee, Hybrid local polynomial wavelet shrinkage: Wavelet regression with automatic boundary adjustment, Comput. Stat. Data Anal. 48 (2005) 809–819.
[10] S.H. Oh, P. Naveau and G. Lee, Polynomial boundary treatment for wavelet regression, Biometrika 88(1) (2001) 291–298.
[11] R. Porto, P.A. Moretin, D.B. Percival and E.C. Aubin, Wavelet shrinkage for regression models with random design and correlated errors, Brazil. J. Probab. Stat. 30(4) (2016) 614–652.
[12] R. Porto and P. Morettin, Wavelet regression with correlated errors on a piecewise Holder class, Stat. Probab. Lett. 78(16) (2008) 2739–2743.
[13] O. Shestakov, Wavelet thresholding risk estimate for the model with random samples correlated noise, Math. 8 (3) (2020) 377.
[14] F. Xiao and Y. Zhang, A Comparative study thresholding methods in wavelet-based image denoising, Procedia Engin. 15 (2011) 3998–4003.
[15] L.J. Yi, L. Hong, Y. Dong and Z.Y. Sheng, A new wavelet threshold function and denoising application, Math. Prob. Engin. 2016 (2016) Article ID 3195492.
Volume 13, Issue 1
March 2022
Pages 1855-1862
  • Receive Date: 01 October 2021
  • Accept Date: 31 October 2021