Deducing and Estimating Nonparametric Signal in Semiparametric Regression Model──Method of Cubic Splines Interpolation

This paper considers the semiparametric regression model y_i= X _i^Tβ+s(t_i)+e_i(for i=1,2,...,n). Where s_i=s(t_i) denotes the nonparametric signal of the observation and y_i a number relating to the observation at t_i, X _i∈R^p(n > p), β=(β₁,...,β_p)^T is parameter vector with p denoting the number of parameters, e_i denotes the noise and is assumed to be independently N(0,σ_i²) distributed.