Math @ Duke

Publications [#332363] of David B. Dunson
search arxiv.org.Papers Published
 Wheeler, MW; Dunson, DB; Herring, AH, Bayesian Local Extremum Splines.,
Biometrika, vol. 104 no. 4
(December, 2017),
pp. 939952, Oxford University Press (OUP)
(last updated on 2019/05/23)
Abstract: We consider shape restricted nonparametric regression on a closed set [Formula: see text], where it is reasonable to assume the function has no more than H local extrema interior to [Formula: see text]. Following a Bayesian approach we develop a nonparametric prior over a novel class of local extremum splines. This approach is shown to be consistent when modeling any continuously differentiable function within the class considered, and is used to develop methods for testing hypotheses on the shape of the curve. Sampling algorithms are developed, and the method is applied in simulation studies and data examples where the shape of the curve is of interest.


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