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Local Asymptotics of P-splines

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abstract

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.

fields

stat.ME 1

years

2025 1

verdicts

CONDITIONAL 1

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  • FLAME: A Model for Duration-Dependent Risk Accumulation in Episodic Temporal Exposures stat.ME · 2025-06-28 · conditional · none · ref 47 · internal anchor

    FLAME models outcome risk as a sum of an unknown duration-response curve over individual exposure episodes, and its cardiac surgery application estimates that sustained hypotension raises AKI risk more per minute than fragmented hypotension, with wide credible intervals.