| Autor: |
Laha N; Department of Biostatistics, Harvard University, 677 Huntington Ave, Boston, MA 02115., Miao Z; Statistics, Box 354322, University of Washington, Seattle, WA 98195-4322., Wellner JA; Statistics, Box 354322, University of Washington, Seattle, WA 98195-4322. |
| Jazyk: |
angličtina |
| Zdroj: |
Journal of statistical planning and inference [J Stat Plan Inference] 2021 Dec; Vol. 215, pp. 127-157. Date of Electronic Publication: 2021 Mar 13. |
| DOI: |
10.1016/j.jspi.2021.03.001 |
| Abstrakt: |
We introduce new shape-constrained classes of distribution functions on R , the bi- s *-concave classes. In parallel to results of Dümbgen et al. (2017) for what they called the class of bi-log-concave distribution functions, we show that every s -concave density f has a bi- s *-concave distribution function F for s * ≤ s /( s + 1). Confidence bands building on existing nonparametric confidence bands, but accounting for the shape constraint of bi- s *-concavity, are also considered. The new bands extend those developed by Dümbgen et al. (2017) for the constraint of bi-log-concavity. We also make connections between bi- s *-concavity and finiteness of the Csörgő - Révész constant of F which plays an important role in the theory of quantile processes. |
| Databáze: |
MEDLINE |
| Externí odkaz: |
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