Statistics Seminars: Confidence Sets in Boundary and Set Estimation
5 June 2009 15:15 in CM107
The ability to estimate a set and its boundary is of primary importance in many fields. As an example, consider estimating the domain of covariates which yield dangerous blood pressure levels.
Here we consider inference of level and sublevel sets of a function by so-called "plug-in" estimators: the level and sublevel sets of a uniformly consistent estimator. We give conditions for strong consistency of these estimators and introduce a method to construct confidence sets. Our results also provide an approach to statistical inference for (compact) random closed sets and their boundaries.
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