Adaptive Estimation of Periodic Regression Model in Short Panel Data

This paper proposes the use of the adaptive estimation method for estimating the periodic regression parameters in short panel data. This will go through three phases. The first phase aims to show that the periodic regression model verifies the Uniform Local Asymptotic Normality (ULAN), the second phase focuses on constructing the local asymptotically Minimax (LAM) estimators, and the last phase deals with constructing the Adaptive Estimators (AE) of the periodic regression model using the results of phase one and phase two. The results obtained in the simulation show that the Adaptive Estimator is always better than the Least Squares Estimator. The AE is more efficient in the case of an asymmetric score function. Real data are used to compare the two methods and show that the periodic coefficient regression model outperforms both traditional regression and random regression models.