On change-point perspectives in multiple testing and weak signal inference

Kostic, Anica (2022) On change-point perspectives in multiple testing and weak signal inference. PhD thesis, London School of Economics and Political Science.

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Abstract

This thesis studies the problem of multiple testing from the change-point perspective, and the problem of inference in the Gaussian sequence model. In the first part of the thesis, we propose a method for estimating the proportion of false null hypotheses among a large number of independently tested hypotheses. The idea is to consider the sequence of sorted p-values as an approximately piecewise linear function with one change-point in slope. We propose an estimator for this change point, which can be further used in combination with Storey’s family of estimators to get the estimator of the false null proportion. Our proposed estimator is conservative and we provide consistency results using the tools from the theory of quantile processes. We compare our estimator to various others proposed in the literature through simulations. Secondly, building on the ideas from the first part, we consider possible applications of some recent multiple change-point methods in multiple testing. We propose to use algorithms for estimating multiple change-points in mean on the sequence of p-values spacings, thus approximating the local FDR with a piecewise constant function. This naturally divides p-values into groups based on their significance. Additionally, we highlight some lesser-known existing change-point interpretations of the global testing methods. Lastly, we propose a thresholding method for inference in the Gaussian sequence model. We analyse it from both multiple testing and signal estimation perspective, and consider its asymptotic behaviour. Starting from the full sequence of values, the method sequentially excludes the largest values one by one, until the remaining values resemble noise. The idea is to consider values in groups in order to retain more signals in the case when signal is weak but dense, shared among many coordinates. We consider a possible application in the change point literature.

Item Type:	Thesis (PhD)
Additional Information:	© 2022 Anica Kostic
Library of Congress subject classification:	Q Science > QA Mathematics
Sets:	Departments > Statistics
Supervisor:	Fryzlewicz, Piotr
URI:	http://etheses.lse.ac.uk/id/eprint/4492

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