(in Notes and Comments)
Convergence Rates of SNP Density Estimators
Victor M. Fenton, A. Ronald Gallant
Econometrica, Vol. 64, No. 3. (May, 1996),
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