(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.


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