Asymptotic normality of pseudo-LS estimator for partly linear autoregression models

Consider the model Yt = [beta]Yt-1 + g(Yt-2) + [var epsilon]t for t [greater-or-equal, slanted] 3. Here g is an unknown function, [beta] is an unknown parameter to be estimated and [var epsilon]t are i.i.d. random error with zero 0 and variance [sigma]2 and [var epsilon]t are independent of Ys for all t [greater-or-equal, slanted] 3 and s = 1, 2. A class of asymptotically normal estimators of [beta] are directly obtained based on piecewise polynomial approximator of g and the model . The asymptotic normality of pseudo-LS (PLS) estimator of [beta] and an estimator of [sigma]2 are investigated.