Local composite quantile regression estimation of time-varying parameter vector for multidimensional time-inhomogeneous diffusion models

Abstract

This paper is dedicated to the study of the composite quantile regression (CQR) estimations of time-varying parameter vectors for multidimensional diffusion models. Based on the local linear fitting for parameter vectors, we propose the local linear CQR estimations of the drift parameter vectors, and verify their asymptotic biases, asymptotic variances and asymptotic normality. Moreover, we discuss the asymptotic relative efficiency (ARE) of the local linear CQR estimations with respect to the local linear least-squares estimations. We obtain that the local estimations that we proposed are much more efficient than the local linear least-squares estimations. Simulation studies are constructed to show the performance of the estimations proposed.

Keywords:

• multidimensional diffusion model
• time-dependent parameter vector
• composite quantile regression estimation
• asymptotic normality
• asymptotic relative efficiency

2010 AMS Subject Classification:

• Primary: 62M05
• Secondary: 62F12

Acknowledgements

The authors are deeply indebted to the anonymous referee for his/her helpful suggestions and valuable comments on this manuscript.

This work is supported by the National Natural Science Foundation (NNSF) of China (No. 11171221); Shanghai Leading Academic Discipline Project (No. XTKX2012).