UBC Theses and Dissertations
Switching nonparametric regression models Pedroso Estevam de Souza, Camila
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.
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