Consider the semiparametric regression model Yi = xi′β + g(ti) + ei for i = 1, 2, . . . , n. Here the design points (xi, ti) are known and nonrandom and the ei are iid random errors with Ee1 = 0 and Ee1 2 = σ2 < ∞. Based on g(·) approximated by a B-spline function, we consider using a test statistic for testing H0 : β = 0. Meanwhile, an adaptive parametric test statistic is constructed and a large sample study for this adaptive parametric test statistic is presented.
- Adaptive estimation
- Asymptotic distribution
- B-spline smoothing
- Nonparametric regression technique