Statistical inference for the partially linear single-index model of panel data with serially correlated error structure

Due to its flexibility, a partially linear single-index model arises in many contemporary scientific endeavors. In this paper, we set foot on its inference under settings of panel data and a serially correlated error component structure. By combining the local polynomial technique with the bias-corrected generalized estimating equations, we propose a feasible weighted generalized estimating equation estimation (GEE-FW) for unknown regression parameters. The GEE-FW is shown to be asymptotically normal and more efficient than the unweighted generalized estimating equation estimation based on working independence. Moreover, a two-stage local linear generalized estimating equation estimation (GEE-TS) of the unknown link function is also proposed, which takes the contemporaneous correlation into account and achieves an increase in its estimated efficiency. The asymptotic property of the GEE-TS is established as well and we show that it is asymptotically more efficient than the one which ignores the contemporaneous correlation. Conducted numerical simulation studies and actual data analysis show that the proposed estimation methods are effective and have good performance in both theory and application.