Consider the regression model Y i = g(t i) + e i for i = 1,...,n. Here -∞ < Y i, e i < ∞, t i ∈ T ⊂ R d, g ∈ H, and H is a specified class of continuous functions from T to R. Based on a finite series expansion g̃ n of g, an M-estimate ĝ n of g is constructed, and the asymptotic normality of the estimate is investigated. Meanwhile, a test statistic for testing H 0 : g(·) = g 0(·) (a known function) is discussed. We also consider M-estimates for semiparametric regression models and show that they are consistent and asymptotically normal.
|Number of pages||15|
|Publication status||Published - 1 Oct 1997|
- Asymptotic normality
- Nonparametotic regression model
- Semiparametric regression model
- Spline smoothing technique