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Wang K, Ghosal S. Posterior contraction and testing for multivariate isotonic regression. Electron J Stat 2023. [DOI: 10.1214/23-ejs2115] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/05/2023]
Affiliation(s)
- Kang Wang
- Department of Statistics, North Carolina State University, Raleigh, NC 27695, U.S.A
| | - Subhashis Ghosal
- Department of Statistics, North Carolina State University, Raleigh, NC 27695, U.S.A
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Chakraborty M, Ghosal S. Convergence rates for Bayesian estimation and testing in monotone regression. Electron J Stat 2021. [DOI: 10.1214/21-ejs1861] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
Affiliation(s)
- Moumita Chakraborty
- Department of Statistics, North Carolina State University, Raleigh, NC 27695, U.S.A
| | - Subhashis Ghosal
- Department of Statistics, North Carolina State University, Raleigh, NC 27695, U.S.A
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Rohrbeck C, Costain DA, Frigessi A. Bayesian spatial monotonic multiple regression. Biometrika 2018. [DOI: 10.1093/biomet/asy019] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Affiliation(s)
- C Rohrbeck
- Department of Mathematics and Statistics, Lancaster University, Bailrigg, Lancaster, U.K
| | - D A Costain
- Department of Mathematics and Statistics, Lancaster University, Bailrigg, Lancaster, U.K
| | - A Frigessi
- Department of Biostatistics, University of Oslo, PB 1122 Blindern, 0317 Oslo, Norway
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Abstract
SummaryWe consider shape-restricted nonparametric regression on a closed set $\mathcal{X} \subset \mathbb{R},$ where it is reasonable to assume that the function has no more than $H$ local extrema interior to $\mathcal{X}$. 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 modelling any continuously differentiable function within the class considered, and we use itto 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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Affiliation(s)
- M W Wheeler
- National Institute for Occupational Safety and Health, 1150 Tusculum Avenue, MS C-15, Cincinnati, Ohio 45226, U.S.A.
| | - D B Dunson
- Department of Statistical Science, Duke University, Box 90251, Durham, North Carolina 27708, U.S.A.
| | - A H Herring
- Department of Statistical Science, Duke University, Box 90251, Durham, North Carolina 27708, U.S.A.
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