E-Books →ORTHONORMAL SERIES ESTIMATORS

Free Download Odile Marie-thérèse Pons, "ORTHONORMAL SERIES ESTIMATORS"
English | ISBN: 9811210683 | 2019 | 304 pages | PDF | 3 MB
The approximation and the estimation of nonparametric functions by projections on an orthonormal basis of functions are useful in data analysis. This book presents series estimators defined by projections on bases of functions, they extend the estimators of densities to mixture models, deconvolution and inverse problems, to semi-parametric and nonparametric models for regressions, hazard functions and diffusions. They are estimated in the Hilbert spaces with respect to the distribution function of the regressors and their optimal rates of convergence are proved. Their mean square errors depend on the size of the basis which is consistently estimated by cross-validation. Wavelets estimators are defined and studied in the same models.