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Delecroix, Michel
Protopopescu, Camelia
Year of Publication: 
Series/Report no.: 
Discussion Papers, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes 2000,7
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.
nonparametric regression
orthonormal series estimators
least squares
almost sure consistency
convergence rates
trigonometric series
Legendre polynomials
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Document Type: 
Working Paper

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