Switching nonparametric regression models for multi-curve data

We develop and apply an approach for analyzing multi-curve data where each curve is driven by a latent state process. The state at any particular point determines a smooth function, forcing the individual curve to switch from one function to another. Thus each curve follows what we call a switching nonparametric regression model. We develop an EM algorithm to estimate the model parameters. We also obtain standard errors for the parameter estimates of the state process. We consider three types of hidden states: those that are independent and identically distributed, those that follow a Markov structure, and those that are independent but with distribution depending on some covariate(s). A simulation study shows the frequentist properties of our estimates. We apply our methods to a building's power usage data. The Canadian Journal of Statistics 45: 442-460; 2017 (c) 2017 Statistical Society of Canada