LOWLAD: a locally weightedL 1 smoothing spline algorithm with cross validated choice of smoothing parameters

The computation ofL₁ smoothing splines on large data sets is often desirable, but computationally infeasible. A locally weighted, LAD smoothing spline based smoother is suggested, and preliminary results will be discussed. Specifically, one can seek smoothing splines in the spacesW_m(D), with [0, 1]ⁿD. We assume data of the formy_i=f(t_i)+_i,i=1,..., N with {t_i}_i=1^ND, the _i are errors withE(_i)=0, andf is assumed to be inW_m. An LAD smoothing spline is the solution,s, of the following optimization problem

Keywords:	Least absolute deviations  robust regression  smoothing and regression splines  thin plate splines  lowess  cross validation  nonparametric estimation
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