Local Asymptotics of P-splines

Details Local Asymptotics of P-splines Local Asymptotics of P-splines

2012-01-03

arxiv.org/abs/1201.0708v2

Mathematics

Statistics Theory

36 pages, 1 figure

Scientific paper

This report studies local asymptotics of P-splines with $p$th degree B-splines and a $m$th order difference penalty. Earlier work with $p$ and $m$ restricted is extended to the general case. Asymptotically, penalized splines are kernel estimators with equivalent kernels depending on $m$, but not on $p$. A central limit theorem provides simple expressions for the asymptotic mean and variance. Provided it is fast enough, the divergence rate of the number of knots does not affect the asymptotic distribution. The optimal convergence rate of the penalty parameter is given.

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