Doukhan, Paul; León, José Rafael Quadratic deviation of projection density estimates. (English) Zbl 0812.62043 REBRAPE 7, No. 1, 37-63 (1993). 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. Reviewer: M.Denker (Göttingen) Cited in 1 Document MSC: 62G07 Density estimation 62G20 Asymptotic properties of nonparametric inference 60F05 Central limit and other weak theorems Keywords:density estimation of projections; quadratic deviation; rate of convergence; central limit result; compact Riemannian manifolds; wavelet functions Citations:Zbl 0133.118 PDFBibTeX XMLCite \textit{P. Doukhan} and \textit{J. R. León}, REBRAPE 7, No. 1, 37--63 (1993; Zbl 0812.62043)