  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 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 the well-known motorcycle
data set treating the data as coming from more than one simulated accident run
with unobserved run labels.
