Consistency of a least squares orthonormal series estimator for a regression function - Michel Delecroix; Camelia Protopopescu (Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes, 2000)
This paper establishes the almost. sure consistency of least. squares regression series estimators, in the L2-norm and the sup-norm, under very large assumptions on the underlying model. Three examples are considered in order to illustrate the general results: trigonometric series, Legendre polynomials and wavelet. series estimators. Then optimal choices for the number of functions in the series are discussed and convergence rates are derived. It is shown that. for the wavelet. case, the best. possible convergence rate is attained.
urn:nbn:de:kobv:11-10047116
Keywords: 330; nonparametric regression; orthonormal series estimators; least squares; almost sure consistency; convergence rates; trigonometric series; Legendre polynomials; wavelets