Switching nonparametric regression models

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Switching nonparametric regression models

TitleSwitching nonparametric regression models
Publication TypeJournal Article
Year of Publication2014
Authorsde Souza, CPE, Heckman, NE
Date PublishedOCT 2
Type of ArticleArticle
KeywordsEM algorithm, latent variables, machine learning, mixture of Gaussian processes, motorcycle data, nonparametric regression
AbstractWe propose a methodology to analyse 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. The states form a stochastic process and their possible values are j=1, horizontal ellipsis , 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. We develop an Expectation-Maximisation algorithm to estimate the parameters of the latent state process and the functions corresponding to the J states. We also obtain standard errors for the parameter estimates of the state process. We conduct simulation studies to analyse the frequentist properties of our estimates. We also apply the proposed methodology to the well-known motorcycle dataset treating the data as coming from more than one simulated accident run with unobserved run labels.