Estimation of the regression function by Legendre wavelets

We estimate a function f with n independent observations by using legendrewavelets operational matrices. the function f is approximated withthe solution of a special minimization problem. we introduce an explicitexpression for the penalty term by legendre wavelets operational matrices.also, we obtain a new upper bound on the approximation error of adifferentiable function f using the partial sums of the legendre wavelets.the validity and ability of these operational matrices are shown by severalexamples of real-world problems with some constraints. an accurate approximationof the regression function is obtained by the legendre waveletsestimator. furthermore, the proposed estimation is compared with a nonparametricregression algorithm and the capability of this estimation isillustrated.