We propose a new method to find spatially adaptive smoothing splines. This new method breaks down the interval [0, 1] into p disjoint sub-intervals. Then we define p functional components in [0, 1], which have two important features. First, the purpose of each of these p components is to estimate the true function locally, i.e., in only one of the sub-intervals. Second, even though all components are defined on the entire domain, i.e. [0, 1], a component has curvature only in one of the aforementioned intervals. The p local estimates are then added together to produce a function estimate over the entire [0, 1] interval. In the proposed method, the additional flexibility that comes from finding these p local functional estimates does not come at any additional computational cost. In spite of having p components there is no need to specify (e.g., choose via cross validation) p smoothing parameters. Theory from COmponent Selection and Shrinkage Operator (COSSO), reduces the problem of specifying these p smoothing parameters to specifying only one smoothing parameter without a loss in flexibility. In fact, empirical studies indicate superior performance of COSSO in the additive model framework over that for the traditional additive model.
Level of Degree
Mathematics & Statistics
First Committee Member (Chair)
Second Committee Member
Third Committee Member
Smoothing (Statistics), Estimation theory, Regression analysis, Nonparametric statistics.
Nosedal-Sanchez, Alvaro. "Adaptive weighting for flexible estimation in nonparametric regression models.." (2011). https://digitalrepository.unm.edu/math_etds/59