Optimal Confidence Bands for Shape-Restricted Curves
By L. Duembgen. 2003
69 citations recorded by the source corpus.
Let Y be a stochastic process on [0,1] satisfying dY(t)=n 1/2 f(t)dt+dW(t) , where n≥1 is a given scale parameter (`sample size'), W is standard Brownian motion and f is an unknown function. Utilizing suitable multiscale tests, we construct confidence bands for f with guaranteed given coverage probability, assuming that f is isotonic or convex. These confidence bands are computationally feasible and shown to be asymptotically sharp optimal in an appropriate sense.
Subfields: Applied Mathematics, Mathematical Physics, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/aa0098b6fde2d7493adf12503324abb237598b9c
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In Applied Mathematics
- Wei Biao Wu
- Adityanand Guntuboyina
- Bodhisattva Sen
- Zhibiao Zhao
- Xiaofeng Shao
- David Degras
- Xiaohui Chen
- Zhou Zhou
In Mathematical Physics
- Zhibiao Zhao
- Adityanand Guntuboyina
- Bodhisattva Sen
- Wei Biao Wu
- Xiaofeng Shao
- Richard A. Davis
- Magda Peligrad
- Heng Liu
In Statistics and Probability
- Adityanand Guntuboyina
- Bodhisattva Sen
- Zhibiao Zhao
- Wei Biao Wu
- Pierre C. Bellec
- Richard J. Samworth
- Tommaso Cai
- Andreas Hagemann
Citations in the corpus
- CONFIDENCE BANDS IN DENSITY ESTIMATION (2010, unknown): “Here some positive results are possible; we refer to Hengartner and Stark (1995), Dümbgen (2003) and Davies, Kovac and Meise (2009).”
- Inference of trends in time series (2007, background): “…of independent errors, the construction of SCBs has been discussed by Johnston (1982), Härdle (1989), Knafl et al. (1985), Hall and Titterington (1988), Härdle and Marron (1991), Eubank and Speckman (1993), Sun and Loader (1994), Xia (1998), Cummins et al. (2001) and Dümbgen (2003) among others.”
- Nonparametric Shape-Restricted Regression (2017, methodology): “In [42], utilizing suitable multiscale tests, the author constructs confidence bands for f that are locally adaptive in a certain sense (to the underlying smoothness in f) and have guaranteed coverage, assuming that f is isotonic or convex.”