(in Notes and Comments)
Convergence Rates of SNP Density Estimators
Victor M. Fenton, A. Ronald Gallant
Econometrica, Vol. 64, No. 3. (May, 1996),
pp. 719-727.
Abstract
Convergence rates are derived for the SNP density estimator.
It is a nonparametric density estimator that has been used in
economics, finance, and the health sciences in applications requiring
its compatibility with maximum likelihood estimation. It is computed
by truncating a Hermite series expansion at a point dependent upon
sample size; squaring the polynomial part of the expansion, which
enforces positivity; and determining the coefficients of the expansion
by quasi maximum likelihood. We obtain L1-norm
convergence rates when the truncation point is set to a fractional
power of the sample size. The rates are similar
to the L1 rates for kernel estimators, which are optimal.
Keywords: Nonparametric, density estimation, SNP, rates of
convergence