In this paper we deepen the study of the nonlinear principal components introduced by Salinelli in 1998, referring to a real random variable. New insights on their probabilistic and statistical meaning are given with some properties. An estimation procedure based on spline functions, adapting to a statistical framework the classical Rayleigh–Ritz method, is introduced. Asymptotic properties of the estimator are proved, providing an upper bound for the rate of convergence under suitable mild conditions. Some applications to the goodness-of-fit test and the construction of bivariate distributions are proposed.
@article{1281100394,
author = {Goia, Aldo and Salinelli, Ernesto},
title = {Optimal nonlinear transformations of random variables},
journal = {Ann. Inst. H. Poincar\'e Probab. Statist.},
volume = {46},
number = {1},
year = {2010},
pages = { 653-676},
language = {en},
url = {http://dml.mathdoc.fr/item/1281100394}
}
Goia, Aldo; Salinelli, Ernesto. Optimal nonlinear transformations of random variables. Ann. Inst. H. Poincaré Probab. Statist., Tome 46 (2010) no. 1, pp. 653-676. http://gdmltest.u-ga.fr/item/1281100394/