Is this the least squares estimate?

• 成果类型: Article
• 署名作者: Demidenko, E
• 署名单位: Dartmouth College; Dartmouth College
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/87.2.437
• 发表日期: 2000
• 页码: 437452
• 关键词: maximum-likelihood estimate; EXISTENCE

摘要

It is shown that the sum of squares can have several local minima with a positive probability for any intrinsically nonlinear regression with infinite tails. Therefore, the availability of global criteria is crucial. The concept of the local convexity level for the sum of squares in nonlinear regression models is introduced, A general formula for this local convexity level is derived and it is shown that the local convexity level is equal to the minimum of the squared radius of the full curvature of the expectation surface of the nonlinear regression.,Two general global criteria are formulated. The ideas are illustrated by four types of nonlinear model, namely polylinear, power, linear hi-regression and exponential regression models. The suggested global criteria are shown to work well for real-life data.