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Quadratic deviation of projection density estimates. (English) Zbl 0812.62043

Authors’ summary: We give here a technique of density estimation of projections generalizing that given by N. N. Chentsov [Sov. Math. Doklady 3, 1559-1562 (1963); translation from Doklady Akad. Nauk SSSR 147, 45-48 (1962; Zbl 0133.118)]. Simple assumptions imply an asymptotically Gaussian behaviour for the quadratic deviation of those estimates. Windows estimates given are optimal in some cases and a rate of convergence is given in the central limit result. These results are applied to compact Riemannian manifolds such as the multidimensional torus or sphere, to associated wavelet functions related to a multiscale analysis, to Hermite polynomials and to orthogonal polynomials such as Legendre polynomials.

MSC:

62G07 Density estimation
62G20 Asymptotic properties of nonparametric inference
60F05 Central limit and other weak theorems

Citations:

Zbl 0133.118
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