Estimation in Single-Index Panel Data Models with Heterogeneous Link Functions

In this paper, we study semiparametric estimation for a single-index panel data model where the nonlinear link function varies among the individuals. We propose using the refined minimum average variance estimation method to estimate the parameter in the single-index. As the cross-section dimension N and the time series dimension T tend to infinity simultaneously, we establish asymptotic distributions for the proposed estimator. In addition, we provide a real-data example to illustrate the finite sample behaviour of the proposed estimation method.