Cumulative estimation in semi-parametric models - (Non-parametric estimator base for a general weight function)

Consider the semi-parametric model l(i) = A(i)(T) X + s(t(i)) + Delta(j) (i = 1, (...) ,n). Firstly, the cumulative estimation method of linear model is applied to the semi-parametric model, moreover, a general weight function is chosen as the non-parametric estimator, both estimators of parameter X and non-parameter s(t(i)) are obtained. Secondly, some statistical properties of estimators are discussed. Finally, an example is imitated, which shows validity of the cumulative method.