Testing serial correlation in semiparametric varying-coefficient partially linear EV models

This paper studies estimation and serial correlation test of a semiparametric varying-coefficient partially linear EV model of the form Y = (XB)-B-tau + Z(tau)a(T) + 6, = X + 77 with the identifying condition E[(epsilon, eta(tau))(tau) = 0, Cov[epsilon, eta(tau))(tau)] =sigma I-2(p+1). The estimators of interested regression parameters sigma(2) and the model error variance sigma(2), as well as the nonparametric components alpha(T), are constructed. Under some regular conditions, we show that the estimators of the unknown vector beta and the unknown parameter sigma(2) are strongly consistent and asymptotically normal and that the estimator of alpha(T) achieves the optimal strong convergence rate of the usual nonparametric regression. Based on these estimators and asymptotic properties, we propose the V-N,V-p test statistic and empirical log-likelihood ratio statistic for testing serial correlation in the model. The proposed statistics are shown to have asymptotic normal or chi-square distributions under the null hypothesis of no serial correlation. Some simulation studies are conducted to illustrate the finite sample performance of the proposed tests.