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The not-so-smoother

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Title: The not-so-smoother
Author: Eveson, Jennifer Paige
Degree: Master of Science - MSc
Program: Statistics
Copyright Date: 1996
Issue Date: 2009-02-17
Series/Report no. UBC Retrospective Theses Digitization Project [http://www.library.ubc.ca/archives/retro_theses/]
Abstract: In this thesis, a local smoothing method, termed the not-so-smoother, designed to estimate discontinuous regression functions is proposed. Local smoothing techniques estimate the regression function at a given point by finding the "best fit" through the observations within a fixed neighbourhood of the point. The "best fit" can be the best constant fit (which gives the moving average smoother), the best linear fit, the best kdegree polynomial fit, et cetera. The not-so-smoother finds the best local broken constant fit, a piecewise constant function with exactly one simple discontinuity. Unlike any of the traditional local smoothing methods, the not-so-smoother uses discontinuous local fits and, therefore, has the ability to preserve discontinuities in the function. Consistency of the not-so-smoother under general conditions is proven. Performance of the smoother on simulated data, both continuous and discontinuous, is demonstrated, and an application to a real data set of electric current recordings through an ion channel in a cell membrane is also shown. Variations of the not-so-smoother which can lead to improved performance in certain situations are investigated.
Affiliation: Science, Faculty of
URI: http://hdl.handle.net/2429/4736
Scholarly Level: Graduate

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