Estimation of the regression function by Legendre wavelets

Document Type : Research Article


1 Department of Mathematic, Graduate University of Advanced Technology, Kerman, Iran.

2 Department of Applied Mathematics and Mahani Mathematical Research Center, Shahid Bahonar University of Kerman, Kerman, Iran.


We estimate a function f with N independent observations by using Leg-endre wavelets operational matrices. The function f is approximated with the solution of a special minimization problem. We introduce an explicit expression for the penalty term by Legendre wavelets operational matrices. Also, we obtain a new upper bound on the approximation error of a differentiable function f using the partial sums of the Legendre wavelets. The validity and ability of these operational matrices are shown by several examples of real-world problems with some constraints. An accurate ap-proximation of the regression function is obtained by the Legendre wavelets estimator. Furthermore, the proposed estimation is compared with a non-parametric regression algorithm and the capability of this estimation is illustrated.


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