Fast and Accurate Inference for the Smoothing Parameter in Semiparametric Models
Welsh, Alan and Martin, Michael and hazelton, Martin and Curran, James
A fast and accurate method of confidence interval construction for the smoothing parameter in penalised 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 maximum likelihood (ML), restricted ML (REML), generalized cross validation (GCV) and Akaike's information criteria (AIC). Simulation 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 well-known fossil data. Giving a range of plausible smoothed values in this instance can help answer questions about the statistical significance of apparent features in the data.
R. Paige and A. A. Trindade, "Fast and Accurate Inference for the Smoothing Parameter in Semiparametric Models," Australian and New Zealand Journal of Statistics, Wiley-Blackwell, Jan 2013.
The definitive version is available at http://dx.doi.org/10.1111/anzs.12008
Mathematics and Statistics
Keywords and Phrases
bootstrap confidence interval; estimating equation; generalised cross-validation; partially linear model; penalised spline regresssion; restricted maximum likelihood; saddlepoint approximation
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