A third order asymptotic comparison of least squares, jack-knifing and cross-validation for error variance estimation in nonlinear regression

Abstract

The residual sum of squares, the jackknifed residual sum and the cross-valida-tory assessment are considered as estimators of the error variance in the nonlinear regression model. On the basis of their asymptotic expansions a third order asymptotic comparison is performed with respect to the median bias and the probability of concentration around the true value. In this sense least squares and jackknifing turn out to be preferably against cross-validation.

AMS 1980 subject classification: 62F10

Keywords:

• Variance estimation
• nonlinear regression
• cross-validation
• jackknifing
• last squares