Switching Nonparametric Regression Models

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. 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. We consider two types of analyses: a single realization case and a replicate case. In the single realization case, we consider one curve switching among J functions. In the replicate case, we have N curves, called replicates, switching between J functions. We develop an EM 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 analyze the frequentist properties of our estimates. We also apply the proposed methodology to two different data sets.