|Constrained Spline Regression and Inference in the Presence of Correlation
Huan Wang, Department of Statistics, Colorado State University
Thursday,April 12, 2012
Distinguishing the trend of data from the pattern of observations is always difficult, especially when the signal is obscured by the correlation of the noise. We propose using spline regression with shape constraints for estimation of trend and inference in the presence of correlated errors when the parametric form of the trend is unknown but we may have some prior information about its shape, such as monotonicity or convexity. Here we also use penalized splines because they are more robust than regression splines and the user choices are simplified to a single penalty parameter. The parameters p and penalty parameter are selected by a correlation-adjusted AIC, simultaneously. The asymptotic properties of projection estimation in regression in the presence of correlation was investigated in a general setting of both classical regression and nonparametric regression. We also proved that the constrained spline regression attains the convergence rate of unconstrained spline regression in presence of correlated errors.