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Regression series estimators: the mise approach
Authors:
Michel Delecrolix a;
Camelia Protopopescu† b
| Affiliations: | a ENSAI, Rue Blaise Pascal, Campus de Ker Lann, Bruz, France |
| b bGREQAM, Centre de la Vieille Charite, Marseille, France |
DOI:
10.1080/10485250108832861
Publication Frequency:
8 issues per year
Subjects:
Mathematical Economics;
Mathematical Finance;
Medical Statistics;
Statistical Theory & Methods;
Statistics;
Statistics for the Biological Sciences;
Stochastic Models & Processes;
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(English)
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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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| Keywords: Nonparametric regression; Orthonormal series estimators; Least squares; Mean integrated squared error; Convergence rates; Trigonometric series; Legendre polynomials; Wavelets |
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