Abstract
We consider a panel data partially linear single-index models (PDPLSIM) with errors correlated in space and time. A serially correlated error structure is adopted for the correlation in time. We propose using a semiparametric minimum average variance estimation (SMAVE) to obtain estimators for both the parameters and unknown link function. We not only establish an asymptotically normal distribution for the estimators of the parameters in the single index and the linear component of the model, but also obtain an asymptotically normal distribution for the nonparametric local linear estimator of the unknown link function. Then, a fitting of spatial and time-wise correlation structures is investigated. Based on the estimators, we propose a generalized F-type test method to deal with testing problems of index parameters of PDPLSIM with errors correlated in space and time. It is shown that under the null hypothesis, the proposed test statistic follows asymptotically a [Formula: see text]-distribution with the scale constant and degrees of freedom being independent of nuisance parameters or functions. Simulated studies and real data examples have been used to illustrate our proposed methodology.
Highlights
We consider a panel data partially linear single-index models (PDPLSIM) with errors correlated in space and time
We propose a generalized F-type test method to deal with testing problems of index parameters of PDPLSIM with errors correlated in space and time
We focused on the estimation and testing for PDPLSIM with errors correlated in space and time
Summary
We propose a semiparametric minimum average variance estimation (SMAVE) method for estimating the parameters θ0, β0 and the link function g(·), combining the methods introduced in [6, 34], and an iterative procedure will be given as detailed below. Let ait = g(xT θ0), bit = g (xT θ0), following the idea of local linear smoothing, we can obtain the estimators of β0 and θ0 by minimizing. They can be solved with simple analytic expressions To this end, we give an iterative procedure as detailed below. For given β and θ, we obtain the local linear estimator of (ait, bit)T by minimizing (6):. (ait, bit)T = (XiTt,∗(θ)MitXit,∗(θ))−1XiTt,∗(θ)Mit(Yit − Zitβ), where Xit,∗(θ) = (eNT , Xit(θ)). For each pair (i, t), substitute (ait, bit)T into (6), and minimize (6) with respect to β and θ to obtain (βT , θT )T =. We can obtain the final estimators βand θby using βand θand the above iterations with the single-index weights. Θ and XiTt θ with β, θand u, we can get the estimator of g(u), which is denoted by g(u)
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
