Bayesian-motivated tests of function fit and their asymptotic frequentist properties
| dc.creator | Aerts, Marc | |
| dc.creator | Claeskens, Gerda | |
| dc.creator | Hart, Jeffrey D. | |
| dc.date | 2005-08-30 | |
| dc.date.accessioned | 2026-07-07T08:07:15Z | |
| dc.date.available | 2026-07-07T08:07:15Z | |
| dc.description | We propose and analyze nonparametric tests of the null hypothesis that a function belongs to a specified parametric family. The tests are based on BIC approximations, π_{BIC}, to the posterior probability of the null model, and may be carried out in either Bayesian or frequentist fashion. We obtain results on the asymptotic distribution of π_{BIC} under both the null hypothesis and local alternatives. One version of π_{BIC}, call it π_{BIC}^*, uses a class of models that are orthogonal to each other and growing in number without bound as sample size, n, tends to infinity. We show that \sqrtn(1-π_{BIC}^*) converges in distribution to a stable law under the null hypothesis. We also show that π_{BIC}^* can detect local alternatives converging to the null at the rate \sqrt\log n/n. A particularly interesting finding is that the power of the π_{BIC}^*-based test is asymptotically equal to that of a test based on the maximum of alternative log-likelihoods. Simulation results and an example involving variable star data illustrate desirable features of the proposed tests. | |
| dc.description | Published at http://dx.doi.org/10.1214/009053604000000805 in 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/0508601 | |
| dc.identifier | http://arxiv.org/abs/math/0508601 | |
| dc.identifier | Annals of Statistics 2004, Vol. 32, No. 6, 2580-2615 | |
| dc.identifier | doi:10.1214/009053604000000805 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/130881 | |
| dc.subject | Statistics Theory | |
| dc.subject | 62G10, 62C10 (Primary) 62G20. (Secondary) | |
| dc.title | Bayesian-motivated tests of function fit and their asymptotic frequentist properties | |
| dc.type | text |