Adaptive multiscale approaches to regression and trend segmentation

Maeng, Hyeyoung (2019) Adaptive multiscale approaches to regression and trend segmentation. PhD thesis, London School of Economics and Political Science.

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Abstract

Data-adaptive modelling has enjoyed increasing popularity across a wide range of statistical problems. This thesis studies three adaptive multiscale approaches, one in regression and two in trend segmentation. We first introduce a way of modelling temporal dependence in random functions, assuming that those random curves are discretised on an equispaced grid. Considering a common dependence structure across the discretised curves, we predict the most recent point from the past observations in the framework of linear regression. Our model partitions the regression parameters into a smooth and a rough regime where rough regression parameters are used for observations located close to the response variable while the set of regression coefficients for the predictors positioned far from the response variable are assumed to be sampled from a smooth function. The smoothness change-point and the regression parameters are jointly estimated, and the asymptotic behaviour of the estimated change-point is presented. The performance of our new model is illustrated through simulations and four real data examples including country fertility data, pollution data, stock volatility series and sunspot number data. Secondly, we study the detection of multiple change-points corresponding to linear trend changes or point anomalies in one-dimensional data. We propose a data-adaptive multiscale decomposition of the data through an unbalanced wavelet transform, hoping that the sparse representation of the data is achieved through this decomposition. The entire procedure consists of four steps and we provide a precise recipe of each.

Item Type:	Thesis (PhD)
Additional Information:	© 2019 Hyeyoung Maeng
Library of Congress subject classification:	Q Science > QA Mathematics
Sets:	Departments > Statistics
Supervisor:	Fryzlewicz, Piotr
URI:	http://etheses.lse.ac.uk/id/eprint/4025

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