Journal of Econometrics

Volume 110, Issue 1, September 2002

J. Econometrics Vol. 110 (1) pp. 27-65

Cross-validated SNP density estimates

a Mark Coppejans
b A. Ronald Gallant

aDepartment of Economics, Duke University, Durham NC 27708-0097, USA
bDepartment of Economics, University of North Carolina, Chapel Hill NC 27599-3305, USA

Received 12 January 2000; revised 17 August 2001; accepted 18 January 2002


We consider cross-validation strategies for the SNP nonparametric density estimator, which is a truncation (or sieve) estimator based upon a Hermite series expansion with coefficients determined by quasi maximum likelihood. Our main focus is on the use of SNP density estimators as an adjunct to EMM structural estimation. It is known that for this purpose a desirable truncation point occurs at the last point at which the ISE curve of the SNP density estimate declines abruptly. We study the determination of the ISE curve for iid data by means of leave-one-out cross-validation and hold-out-sample cross-validation through an examination of their performance over the Marron-Wand test suite and models related to asset pricing and auction applications. We find that both methods are informative as to the location of abrupt drops, but that neither can reliably determine the minimum of the ISE curve. We validate these findings with a Monte Carlo study. The hold-out-sample method is cheaper to compute because it requires fewer nonlinear optimizations. We consider the asymptotic justification of hold-out-sample cross-validation. For this purpose, we establish rates of convergence of the SNP estimator under the Hellinger norm that are of interest in their own right.

JEL Classification: C14; C15

Keyword(s): Cross-validation, seminonparametric, SNP, efficient method of moments, EMM, Hellinger distance, convergence rates