CONSTRAINED SMOOTHING SPLINES
提出一种将参数模型先验信息融入非参数回归的平滑样条方法，估计量为数据拟合与参数模型的凸组合，并给出渐近性质、推断方法和数据驱动的平滑参数选择，最后应用于美国电话行业投资行为建模。
We use smoothing splines to introduce prior information in nonparametric models. The type of information we consider is based on the belief that the regression curve is similar in shape to a parametric model. The resulting estimator is a convex sum of a fit to data and the parametric model, and it can be seen as shrinkage of the smoothing spline toward the parametric model. We analyze its rates of convergence and we provide some asymptotic distribution theory. Because the asymptotic distribution is intractable, we propose to carry out inference with the estimator by using the method proposed by Politis and Romano (1994, Annals of Statistics 22, 2031–2050). We also propose a data-driven technique to compute the smoothing parameters that provides asymptotically optimal estimates. Finally, we apply our results to the estimation of a model of investment behavior of the U.S. telephone industry and we present some Monte Carlo results.