Description
- Abstract:
- This thesis concerns itself with the study of nonparametric simultaneous confidence bands for binary regression and density functions, which can be viewed as a multiple hypothesis problem with infinite number of hypothesis. There are a variety of statistical methods for nonparametrically estimating binary regression and density functions. Although many of these methods come with some notion of statistical confidence, we find that they often perform quite poorly in realistic simulations, since confidence estimates are often based on large sample or dense data assumptions that are rarely satisfied in practice. Furthermore, many of the methods for assessing confidence are prohibitively slow when applied to modern large datasets. We propose a method that permits fast and exact nonparametric confidence bands, which works even in the case of sparse data. We formally derive the bands and we assess their theoretical performance on simulated data sets. We show their practical use in real data for assessing changes in hippocampal place fields across experimental conditions in rats and for assessing changes in firing rates during a learning task in monkeys. These are the datasets that originally motivated our research. Finally, we empirically show that our method is overly conservative. To increase its power, we suggest incorporating bootstrap resampling. This is done in a novel way such that we are estimating a scalar quantity as opposed to estimating an entire distribution. The bootstrap version of our method, which has an increased power, lacks finite sample consistency guarantees, but we outline a proof of its asymptotic consistency.
- Notes:
- Thesis (Ph. D.)--Brown University, 2019
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Citation
Petrovic, Ivana,
"Simultaneous confidence bands in nonparametric binary regression and density estimation"
(2019).
Applied Mathematics Theses and Dissertations.
Brown Digital Repository. Brown University Library.
https://doi.org/10.26300/dqhx-ce26
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Applied Mathematics Theses and Dissertations
Theses and Dissertations for the Applied Mathematics department....