Theory for penalised spline regression

By Peter Hall, Jean D. Opsomer. 2005

97 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/2a8386c7487c274856b6b7758dfe4279f55e0e35

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In Statistics and Probability

Citations in the corpus

Smoothing Parameter and Model Selection for General Smooth Models (2015, background): “rea that can appear co nfusing in the literature. The best mean square error rate achievable by a penalized smoother with two continuous derivatives is O(n−4/5) (Stone, 1982; 6 Speckman, 1985), which Hall and Opsomer (2005) show also applies to penalized cubic regression splines as considered here. ”
Well-Being over the Life Span: Semiparametric Evidence from British and German Longitudinal Data (2009, background): “P-spline regression provides a consistent estimate of η(·) (Yu & Ruppert, 2002; Hall & Opsomer, 2005).”
Determination of linear components in additive models (2011, methodology): “Asymptotic properties and smoothing parameter selection of a penalised spline estimator can be found in Wand (1999) , Hall and Opsomer (2005) , Li and Ruppert (2008) , and Claeskens, Krivobokova, and Opsomer (2008) .”
Some asymptotic results on generalized penalized spline smoothing (2009, methodology): “Originally suggested by O’Sullivan (1986), the approach has achieved general attention with the paper by Eilers & Marx (1996) who phrased the routine as P-spline smoothing.”
On the asymptotics of penalized spline smoothing (2011, background): “Claeskens, Krivobokova, and Opsomer [2] studied bias, variance, and asymptotic rates of the penalized spline estimator under different choices of the number of knots and penalty parameters.”
A Note on Penalized Spline Smoothing With Correlated Errors (2007, background): “Some first results have been given by Cardot (2002), Hall and Opsomer (2005), and Li and Ruppert (2007).”
Simultaneous Confidence Bands for Penalized Spline Estimators (2010, background): “Some first results were presented by Hall and Opsomer (2005), Li and Ruppert (2008), and Kauermann, Krivobokova, and Fahrmeir (2009).”
ON SEMIPARAMETRIC REGRESSION WITH O'SULLIVAN PENALIZED SPLINES (2008, background): “O-splines in terms of estimation performance, perhaps in the spirit of Hall & Opsomer (2005) , would be ideal ‐ although beyond the scope of the current paper.”
Fast bivariate P‐splines: the sandwich smoother (2010, background): “An asymptotic study of univariate penalized splines was achieved only recently (Hall and Opsomer, 2005; Li and Ruppert, 2008; Claeskens et al., 2009; Kauermann et al., 2009; Wang et al., 2011).”
Penalized spline models for functional principal component analysis (2006, methodology): “To apply the asymptotic results for penalized spline regression that were developed for independent data in Hall and Opsomer (2005), we adopt the following notation.”
On the asymptotics of penalized splines (2008, unknown): “Another advantage of our approach over that in Hall & Opsomer (2005) is that we can find the minimum rate at which the number of knots must converge to ∞ in order for the modelling bias to be negligible.”