The DOI matches its Crossref record; 32 of the 32 references it cites were found in a registry or an index.
Local Extremes, Runs, Strings and Multiresolution
Open accessAbstract
The paper considers the problem of nonparametric regression with emphasis on controlling the number of local extremes. Two methods, the run method and the taut-string multiresolution method, are introduced and analyzed on standard test beds. It is shown that the number and locations of local extreme values are consistently estimated. Rates of convergence are proved for both methods. The run method converges slowly but can withstand blocks as well as a high proportion of isolated outliers. The rate of convergence of the taut-string multiresolution method is almost optimal. The method is extremely sensitive and can detect very low power peaks. Section 1 contains an introduction with special reference to the number of local extreme values. The run method is described in Section 2 and the taut-string-multiresolution method in Section 3. Low power peaks are considered in Section 4. Section contains a comparison with other methods and Section 6 a short conclusion. The proofs are given in Section 7 and the taut-string algorithm is described in the Appendix.
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Cites
Density Estimation for Statistics and Data Analysis
Silverman, B. W. (2018) · Routledge eBooks · doi:10.1201/9781315140919 · Cited by 15,796
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Estimation of the Mean of a Multivariate Normal Distribution
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Tukey, J. W. (1977) · International Linear Collider · Cited by 2,155
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Nonparametric Regression and Generalized Linear Models
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INADMISSIBILITY OF THE USUAL ESTIMATOR FOR THE MEAN OF A MULTIVARIATE NORMAL DISTRIBUTION
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Wavelet Shrinkage: Asymptopia?
Donoho, D. L., Johnstone, I. M., Kerkyacharian, G., & Picard, D. (1995) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.2517-6161.1995.tb02032.x · Cited by 1,749
Statistical Inference Under Order Restrictions
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Ramsay, J. O., Hooker, G., Campbell, D., & Cao, J. (2007) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.1467-9868.2007.00610.x · Cited by 613
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Metadata
- Authors
- Davies, P. L., & Kovac, A.
- Venue
- The Annals of Statistics
- Publisher
- Institute of Mathematical Statistics
- Published
- 2001-02-01
- Volume
- 29
- Issue
- 1
- Pages
- 1-65
- ISSN
- 0090-5364 (ISSN-L)
- OpenAlex
- W2162894628
- Cited by
- 265
- References
- 32
- FWCI
- 7.78
- Type
- journal article
- Language
- en
- Open access
- bronze
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Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
