Journal
COMPUTATIONAL STATISTICS & DATA ANALYSIS
Volume 51, Issue 3, Pages 1739-1753Publisher
ELSEVIER
DOI: 10.1016/j.csda.2006.06.015
Keywords
convexity; curvature; global minimization; nonlinear regression; uniqueness; unimodality
Ask authors/readers for more resources
Demidenko [2000. Is this the least squares estimate? Biometrika 87, 437-452] has established the relationship between the curvature of nonlinear regression and the local convexity of a sum of squares: the Hessian matrix is positive definite if the sum of squares is less than the minimum squared radius of the full curvature. In this paper, we continue developing the criteria for the global minimum of the sum of squares in nonlinear regression. In particular, the concept of the local unimodality is introduced; a function is called locally unimodal on a level set if it has a unique local minimum in each component of that level set. We show that the level of the local unimodality of the sum of squares is equal to the minimum squared radius of the intrinsic curvature of the nonlinear regression function. A new class of unidirected nonlinear regression models is introduced with an interpretation in terms of differential geometry. The criteria are illustrated by several popular nonlinear regression models. (c) 2006 Elsevier B.V. All rights reserved.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available