Using Different Threshold Values in Wavelet Reduction Method to Estimate the Nonparametric Regression Model With Correlation in Errors
Mohmmed Salh Abdu Alkareem Mahdi
Ministry of Interior, Directorate of Human Resources, Iraq
Dr. Saad Kadem Hamza
Department of Statistics, College of Administration and Economics University Of Baghdad, Iraq
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The wavelet reduction technique is one of the best techniques used in estimating the
nonparametric regression function, but it is affected in the event that the errors are related, so
(Jonstone) suggested a level-dependent thresholding method to extract the signal from the
associated noise. In this paper, a number of types of thresholds will be selected that reduce the
risk criterion in estimating the nonparametric regression function and in the presence of a
correlation in errors, and these methods are (False Discovery Rate Thresholding), (Bayesshrink
Thresholding) and (Universal Thresholding), as simulation experiments were used using Three
test and correlation functions of type (AR(1)), sample sizes (64, 128) and different noise ratios. It
was found that the best methods were the (False Discovery Rate Thresholding) method, followed
by the (Bayesshrink Thresholding) method, while the comprehensive threshold method declined
in light of Correlation problem at sample size (128).
Keywords: Wavelet Reduction Method; Nonparametric Regression Model; False Discovery Rate Thresholding
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