Estimation of the regression function by Legendre wavelets

Iranian Journal of Numerical Analysis and Optimization

مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 18 اسفند 1400  

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.2022.73876.1079

نویسندگان

Mehdi Hamzehnejad ¹؛ Mohammad Mehdi Hosseini²؛ Abbas Salemi ²

¹Department of Mathematics, Faculty of Science and Modern Technology, Graduate University of Advanced Technology, Kerman, Iran

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

چکیده

In this paper, we estimate a function $f$ with $N$ independent observations by using Legendre 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 approximation 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.

کلیدواژه‌ها

Legendre wavelet؛ Operational matrix؛ Wavelet approximation؛ Regression function؛ Error analysis