Switching nonparametric regression models
department or school: Science, Faculty of
department or school: Statistics, Department of
data provider: DSpace
degree campus: UBCV
creator: Pedroso Estevam de Souza, Camila
issued: 2013-09-26T15:58:58Z
issued: 2013
related degree: Doctor of Philosophy - PhD
degree grantor: University of British Columbia
description: In this thesis, we propose a methodology to analyze data arising from a curve that, over its domain, switches among J states. We consider a sequence of response variables, where each response y depends on a covariate x according to an unobserved state z, also called a hidden or latent state. The states form a stochastic process and their possible values are j=1,...,J. If z equals j the expected response of y is one of J unknown smooth functions evaluated at x. We call this model a switching nonparametric regression model. In a Bayesian switching nonparametric regression model the uncertainty about the functions is formulated by modeling the functions as realizations of stochastic processes. In a frequentist switching nonparametric regression model the functions are merely assumed to be smooth. We consider two different data structures: one with N replicates and the other with one single realization. For the hidden states, we consider those that are independent and identically distributed and those that follow a Markov structure. We develop an EM algorithm to estimate the parameters of the latent state process and the functions corresponding to the J states. Standard errors for the parameter estimates of the state process are also obtained. We investigate the frequentist properties of the proposed estimates via simulation studies. Two different applications of the proposed methodology are presented. In the first application we analyze the well-known motorcycle data in an innovative way: treating the data as coming from J>1 simulated accident runs with unobserved run labels. In the second application we analyze daytime power usage on business days in a building treating each day as a replicate and modeling power usage as arising from two functions, one function giving power usage when the cooling system of the building is off, the other function giving power usage when the cooling system is on.
aggregated CHO: https://circle.library.ubc.ca/rest/handle/2429/45130
note: Switching Nonparametric Regression ModelsbyCamila Pedroso Estevam de SouzaBachelor?s Degree in Statistics, University of Campinas, Brazil, 2005Master?s Degree in Statistics, University of Campinas, Brazil, 2008A THESIS SUBMITTED IN PARTIAL FULFILLMENTOF THE REQUIREMENTS FOR THE DEGREE OFDoctor of PhilosophyinTHE FACULTY OF GRADUATE AND POSTDOCTORALSTUDIES(Statistics)The University Of British Columbia(Vancouver)September 2013c? Camila Pedroso Estevam de Souza, 2013AbstractIn this thesis, we propose a methodology to analyze data arising from a curve that,over its domain, switches among J states. We consider a sequence of responsevariables, where each response y depends on a covariate x according to an unob-served state z, also called a hidden or latent state. The states form a stochasticprocess and their possible values are j = 1, . . . ,J. If z equals j the expected re-sponse of y is one of J unknown smooth functions evaluated at x. We call thismodel a switching nonparametric regression model. In a Bayesian switching non-parametric regression model the uncertainty about the functions is formulated bymodeling the functions as realizations of stochastic processes. In a frequentistswitching nonparametric regression model the functions are merely assumed to besmooth. We consider two different data structures: one with N replicates and theother with one single realization. For the hidden states, we consider those that areindependent and identically distributed and those that follow a Markov structure.We develop an EM algorithm to estimate the parameters of the latent state processand the functions corresponding to the J states. Standard errors for the parameterestimates of the state process are also obtained. We investigate the frequentist prop-erties of the proposed estimates via simulation studies. Two different applicationsof the proposed methodology are presented. In the first application we analyzethe well-known motorcycle data in an innovative way: treating the data…
has type: Thesis/Dissertation
date issued: 2013-11
is shown at: 10.14288/1.0107630
language: eng
degree discipline: Statistics
provider: Vancouver : University of British Columbia Library
publisher: University of British Columbia
rights: Attribution-NonCommercial-NoDerivatives 4.0 International
rights URI: http://creativecommons.org/licenses/by-nc-nd/4.0/
scholar level: Graduate
type: Text
identifier URI: http://hdl.handle.net/2429/45130