COOKIES: By using this website you agree that we can place Google Analytics Cookies on your device for performance monitoring. |

University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > Inference for the mode of a log-concave density: a likelihood ratio test and confidence intervals

## Inference for the mode of a log-concave density: a likelihood ratio test and confidence intervalsAdd to your list(s) Download to your calendar using vCal - Jon August Wellner (University of Washington)
- Tuesday 03 April 2018, 11:00-12:00
- Seminar Room 2, Newton Institute.
If you have a question about this talk, please contact info@newton.ac.uk. STS - Statistical scalability I will discuss a likelihood ratio test for the mode of a log-concave density. The new test is based on comparison of the log-likelihoods corresponding to the unconstrained maximum likelihood estimator of a log-concave density and the constrained maximum likelihood estimator, where the constraint is that the mode of the density is fixed, say at m. The constrained estimators have many properties in common with the unconstrained estimators discussed by Walther (2001), Pal, Woodroofe, and Meyer (2007), Dümbgen and Rufibach (2009), and Balabdaoui, Rufibach and Wellner (2010), but they differ from the unconstrained estimator under the null hypothesis on n^{−1/5} neighborhoods of the mode m. Using joint limiting properties of the unconstrained and constrained estimators we show that under the null hypothesis (and strict curvature of – log f at the mode), the likelihood ratio statistic is asymptotically pivotal: that is, it converges in distribution to a limiting distribution which is free of nuisance parameters, thus playing the role of the chi-squared distribution in classical parametric statistical problems. By inverting this family of tests, we obtain new (likelihood ratio based) confidence intervals for the mode of a log-concave density f. These new intervals do not depend on any smoothing parameters. We study the new confidence intervals via Monte Carlo studies and illustrate them with several real data sets. The new confidence intervals seem to have several advantages over existing procedures. This talk is based on joint work with Charles Doss. This talk is part of the Isaac Newton Institute Seminar Series series. ## This talk is included in these lists:- All CMS events
- Featured lists
- INI info aggregator
- Isaac Newton Institute Seminar Series
- School of Physical Sciences
- Seminar Room 2, Newton Institute
- bld31
Note that ex-directory lists are not shown. |
## Other listsCUED Control Group Seminars Moral Psychology Research Group Cambridge University Somali Society (CUSOMSOC)## Other talksGraphons and Graphexes as Limits of Sparse Graphs: Part II Unlocking medical questions with a developmental biology key Relativity, Quantum Theory and Cryptography fNIRS shines a light on early atypical brain responses in autism Cancer and Metbolism 2018 |