Wavelet Threshold Estimator of Semiparametric Regression Function with Correlated Errors

Abstract

Wavelet analysis is one of the useful techniques in mathematics which is used much in statistics science recently. In this paper, in addition to introduce the wavelet transformation, the wavelet threshold estimation of semiparametric regression model with correlated errors with having Gaussian distribution is determined and the convergence ratio of estimator computed. To evaluate the wavelet threshold estimation, the block function and sinusoidal function are used as objective functions and using the simulation method the average of mean square error and standard deviation of this estimator are compared with the average of mean square error and standard deviation of kernel method. Also, the wavelet semiparametric regression model has been fitted to data on the growth rate of the teeth.

Keywords

• convergence ratio
• correlated errors
• semiparametric regression
• wavelet threshold