Abstract
This paper deals with the study of the MISE asymptotic properties of regression series estimators. For technical reasons, a slightly modified definition of the "classical** orthonormal series estimator is introduced. Upper bounds for the MISE criterion are derived in a general framework, then the result is particularized for trigonometric series, Legendre polynomials and wavelet bases. Sufficient conditions for the MISE consistency, as well as MISE convergence rates, are given in these particular cases.
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