Bandwidth-based nonparametric inference |
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Authors: | David B. Hitchcock |
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Affiliation: | aDepartment of Statistics, University of South Carolina, 216 LeConte College, Columbia, SC 29208, United States |
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Abstract: | Nonparametric curve estimation is an extremely common statistical procedure. While its primary purpose has been exploratory, some advances in inference have been made. This paper provides a critical review of inferential tests that make fundamental use of a key element of nonparametric smoothing, the bandwidth, to determine the significance of certain features. A major focus is on two important problems that have been tackled using bandwidth-based inference: testing for the multimodality of a density and testing for the monotonicity of a regression curve. Early research in bandwidth-based inference is surveyed, as well as recent theoretical advances. Possible future directions in bandwidth-based inference are discussed. |
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Keywords: | Bump hunting Density estimation Monotone nonparametric regression Multimodality Smoothing |
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