半参数模型误差为NA序列时的r阶矩相合性

ON rTH MEAN CONSISTENCY IN SEMIPARAMETRIC REGRESSION MODEL UNDER NA ERROR SEQUENCES

考虑半参数回归模型,其中β∈R为未知回归参数,g(·)为[0,1]上的未知Borel函 数,Antoniads[4]中给出了非参数回归模型的小波估计,本文利用小波光滑方法并综合最小二 乘法给出了β、g(t)的小波估计^β、^g(t),在误差为NA序列时,得到了^β、^g(t)的r(r≥2)阶矩相 合性。

For semiparametric regression model y i=x iβ+g(t i)+e i, i=1,2,…,n , we use the least squares and wavelet smoothing methods to define the estimations and (t) for β and g(t) , and obtain its r th mean consistency under NA error sequences.