Semi-parametric Regression Models And Some Theoretical Studies

This paper studies mainly the theories of the semi -parametric regression model:(1) Under proper conditions, using random weighted way to the estimator of the error density f(x) of the semi-parametric regression model, this paper proved the strong and weak consistent and the asymptotic unbiased property of the weighted kernel estimation fn1(x) of the f(x).(2) In this paper, using [v,g(ti)]n,h = m(v,(1)yi(1)… ,vi(h)yi(h)) to the estimator of β and g(t) of the semi-parametric regression model, and h is the smoothing parameter. Using cross-validation to select h as hn*.Under proper conditions, this paper gives the bounds of hn* , and the convergence rate and the weak consistencyof g(t).(3) Suppose ei (1≤i≤n) are strictly stationary a - mixing time series defined in probability space (Ω, A, P) and valued in R in semi-parametric regression model, when (xi,ti) are fixed design series, using domain polynomial smoothing to estimate the non-parametric part g(t), then using least squares estimator for the parametric part β . The value of the estimator β and g(t) are related with the window width h of the kernel function Kh (t) , and h is a variable parametric. Inthis paper, using cross-validation way to select h ,and then to select the model ,and finally, studies the adaptation of model selection.