Are regression series estimators efficient in practice? A computational comparison study (Q1424608)

Consider the classical problem of estimating an unknown regression function \(g(x)=E(Y_i\mid X_i=x)\) from a sample of independent, identically distributed \(R^2\) random variables \((Y_i,X_i)\) without any parametric restriction on the \((Y_i,X_i)\) distribution. The authors focuse on the practical efficiency of series-type (ST) regression estimators of \(g\) and carried out a simulation study to compare four ST estimators based on different choices of orthonormal bases (namely Legendre polynomials, trigonometric functions, two kinds of Daubechies wavelets) with other two of the most popular nonparametric regression methods: kernel Nadaraya-Watson estimators and spline smoothing. These methods were compared on various samples, choosing empirically parameters for each of the methods, in order to obtain the best performance they can practically provide. It was shown that orthonormal series estimators are competitive in relation to the above mentioned nonparametric procedures. However, no agreement has emerged on the best method, the results being highly dependent on the nature of estimated data.