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Smoothing parameter selection in two frameworks for penalized splines
Author(s) -
Krivobokova Tatyana
Publication year - 2013
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/rssb.12010
Subject(s) - smoothing , estimator , smoothing spline , mathematics , spline (mechanical) , selection (genetic algorithm) , mathematical optimization , model selection , mean squared error , function (biology) , regression , nonparametric regression , statistics , computer science , artificial intelligence , spline interpolation , structural engineering , evolutionary biology , engineering , bilinear interpolation , biology
Summary There are two popular smoothing parameter selection methods for spline smoothing. First, smoothing parameters can be estimated by minimizing criteria that approximate the average mean‐squared error of the regression function estimator. Second, the maximum likelihood paradigm can be employed, under the assumption that the regression function is a realization of some stochastic process. The asymptotic properties of both smoothing parameter estimators for penalized splines are studied and compared. A simulation study and a real data example illustrate the theoretical findings.