Geman, S. | Search NASA

NASA NTRS1982

Cross-validation for densities and regressions

Virtually all nonparametric (infinite dimensional) problems require the choice of a smoothing parameter. It is natural to attempt to use the data to guide the choice of this parameter. The most widely applicable data driven technique is cross validation. The method of cross validation is introduced and results are presented which establish consistency for certain cross validated density estimators and consistency as well as asymptotic normality for rigid regression.

Geman, S.↗

NASA NTRS1982

Characterization of a maximum-likelihood nonparametric density estimator of kernel type

Kernel type density estimators calculated by the method of sieves. Proofs are presented for the characterization theorem: Let x(1), x(2),...x(n) be a random sample from a population with density f(0). Let sigma 0 and consider estimators f of f(0) defined by (1).

Geman, S.↗