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Summary An exposition on the use of O'Sullivan penalized splines in contemporary semiparametric regression, including mixed model and Bayesian formulations, is presented. O'Sullivan penalized splines are similar to P‐splines, but have the advantage of being a direct generalization of smoothing splines. Exact expressions for the O'Sullivan penalty matrix are obtained. Comparisons between the two types of splines reveal that O'Sullivan penalized splines more closely mimic the natural boundary behaviour of smoothing splines. Implementation in modern computing environments such as Matlab , r and bugs is discussed.
Wand et al. (Wed,) studied this question.