Statistical inference for the extended non linear models

Abstract

In this article, an orthogonality-projection-based estimation method is first employed to study an extended non linear model, which can separately estimate the linear and non linear parts without losing some efficiency and increasing computation burden. To overcome the non robustness of classical least squares methods, we further propose a robust and efficient estimation procedure based on the exponential squares loss function, which is robust against outliers or heavy-tailed errors while asymptotically efficient as the non linear least squares estimation under the normal error case. Under some regularity conditions, the asymptotic properties of the proposed estimators are established. In addition, simulation studies are conducted to examine the finite sample performance of the proposed estimation methods.

Keywords:

• Orthogonality-projection
• exponential squares loss
• non linear least squares
• asymptotic properties
• non linear model

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

Yang Zhao’s research was supported by the National Natural Science Foundation of China (12061044, 62163027) and the Social Science Foundation of Jiangxi Province (21JY03).