A finite series approximation technique is introduced. We first apply this approximation technique to a semiparametric single-index model to construct a nonlinear least squares (LS) estimator for an unknown parameter and then discuss the confidence region for this parameter based on the asymptotic distribution of the nonlinear LS estimator. Meanwhile, a computational algorithm and a small sample study for this nonlinear LS estimator are developed. Additionally, we apply the finite series approximation technique to a partially nonlinear model and obtain some new results.
|Number of pages||25|
|Journal||Annals of the Institute of Statistical Mathematics|
|Publication status||Published - 1 Jan 1997|
- Asymptotic normality
- Finite series approximation
- Partially nonlinear model
- Semiparametric single-index regression model