Wild Bootstrap Confidence Bands for Free-knot Spline in Generalized Regression Models
Abstract: It is well known that Free-knot spline introduces flexible location parameters in the polynomial splines in order to capture the nonlinear trend and distinct structure changes. The free location unknowns bring advantages to capture marked data pattern precisely and also unavoidable lethargy and heavy computational cost. In this paper, we proposed a free-knot spline confidence bands via penalized likelihood function maximization procedures. To optimize the complex objective functions efficiently, we borrow the Automatic Differentiation Model Builders proposed by Skaug and Fourier (2006) to approximate the general likelihood functions. Wild bootstrapping algorithms is adopted in order to obtain consistent variance estimates and construct confidence bands in a generalized regression models when variance is a function of its mean. With satisfied performance and improved computation power, the proposed methods have been applied in a general model setting ups in simulation studies and a couple of real data analysis.