Journal Article10.1007/S10463-007-0148-Y
Bayesian isotonic changepoint analysis
TL;DR: A general approach to Bayesian isotonic changepoint problems is developed and it is shown that the proposed Bayesian approach captures the qualitative conclusion about the shape of the trend change.
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Abstract: A general approach to Bayesian isotonic changepoint problems is developed. Such isotonic changepoint analysis includes trends and other constraint problems and it captures linear, non-smooth as well as abrupt changes. Desired marginal posterior densities are obtained using a Markov chain Monte Carlo method. The methodology is exemplified using one simulated and two real data examples, where it is shown that our proposed Bayesian approach captures the qualitative conclusion about the shape of the trend change.
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Citations
M-estimators for isotonic regression
TL;DR: In this paper, the authors proposed a family of robust estimates for isotonic regression called isotonic M-estimators, which is the same as that of Brunk's classical isotonic estimator.
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TL;DR: In this paper, the authors study the asymptotic behavior of a Bayesian nonparametric test of qualitative hypotheses and propose a procedure that is straightforward to implement, which is a great advantage compared to those proposed in the literature.
Bayesian regression with B‐splines under combinations of shape constraints and smoothness properties
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•Posted Content
M-estimators for Isotonic Regression
Abstract: In this paper we propose a family of robust estimates for isotonic regression: isotonic M-estimators. We show that their asymptotic distribution is, up to an scalar factor, the same as that of Brunk's classical isotonic estimator. We also derive the influence function and the breakdown point of these estimates. Finally we perform a Monte Carlo study that shows that the proposed family includes estimators that are simultaneously highly efficient under gaussian errors and highly robust when the error distribution has heavy tails.
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