Alex Trindade
Texas Tech University
Fast and Accurate Inference for the Smoothing Parameter in Semiparametric Models
A fast and accurate method of confidence interval construction for the
smoothing parameter in penalized spline and partially linear models is
proposed. The method is akin to a parametric percentile bootstrap where
Monte-Carlo simulation is replaced by saddlepoint approximation, and
can therefore be viewed as an approximate bootstrap. It is applicable
in a quite general setting, requiring only that the underlying estimator
be the root of an estimating equation that is a quadratic form in normal
random variables. This is the case under a variety of optimality criteria
such as those commonly denoted by ML, REML, GCV, and AIC. Simulations studies
reveal that under the ML and REML criteria, the method delivers a near-exact
performance with computational speeds that are an order of magnitude faster than
existing exact methods, and two orders of magnitude faster than a classical
bootstrap. Perhaps most importantly, the proposed method also offers a computationally
feasible alternative when no known exact or asymptotic methods exist, e.g. GCV
and AIC. An application is illustrated by applying the methodology to the well-known
fossil data. Giving a range of plausible smooths in this instance can help answer questions
about the statistical significance of apparent features in the data.