Goodness-of-fit tests via phi-divergences
| dc.creator | Jager, Leah | |
| dc.creator | Wellner, Jon A. | |
| dc.date | 2006-03-10 | |
| dc.date | 2007-11-22 | |
| dc.date.accessioned | 2026-07-07T08:49:46Z | |
| dc.date.available | 2026-07-07T08:49:46Z | |
| dc.description | A unified family of goodness-of-fit tests based on $ϕ$-divergences is introduced and studied. The new family of test statistics $S_n(s)$ includes both the supremum version of the Anderson--Darling statistic and the test statistic of Berk and Jones [Z. Wahrsch. Verw. Gebiete 47 (1979) 47--59] as special cases ($s=2$ and $s=1$, resp.). We also introduce integral versions of the new statistics. We show that the asymptotic null distribution theory of Berk and Jones [Z. Wahrsch. Verw. Gebiete 47 (1979) 47--59] and Wellner and Koltchinskii [High Dimensional Probability III (2003) 321--332. Birkhäuser, Basel] for the Berk--Jones statistic applies to the whole family of statistics $S_n(s)$ with $s\in[-1,2]$. On the side of power behavior, we study the test statistics under fixed alternatives and give extensions of the ``Poisson boundary'' phenomena noted by Berk and Jones for their statistic. We also extend the results of Donoho and Jin [Ann. Statist. 32 (2004) 962--994] by showing that all our new tests for $s\in[-1,2]$ have the same ``optimal detection boundary'' for normal shift mixture alternatives as Tukey's ``higher-criticism'' statistic and the Berk--Jones statistic. | |
| dc.description | Published in at http://dx.doi.org/10.1214/0009053607000000244 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org) | |
| dc.identifier | https://arxiv.org/abs/math/0603238 | |
| dc.identifier | http://arxiv.org/abs/math/0603238 | |
| dc.identifier | Annals of Statistics 2007, Vol. 35, No. 5, 2018-2053 | |
| dc.identifier | doi:10.1214/0009053607000000244 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/144423 | |
| dc.subject | Statistics Theory | |
| dc.subject | 62G10, 62G20 (Primary) 62G30 (Secondary) | |
| dc.title | Goodness-of-fit tests via phi-divergences | |
| dc.type | text |