Switching nonparametric regression models for multi-curve data

TL;DR

This paper introduces a switching nonparametric regression model for multi-curve data driven by latent states, with an EM algorithm for parameter estimation and applications to power usage data.

Contribution

It proposes a novel model for multi-curve data with switching behaviors and develops an EM algorithm for efficient estimation of model parameters.

Findings

The EM algorithm effectively estimates model parameters.

Simulation studies confirm the estimator's good properties.

Application to power data demonstrates practical utility.

Abstract

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 several types of state processes: independent and identically distributed, independent but depending on a covariate and Markov. Simulation studies show the frequentist properties of our estimates. We apply our methods to a data set of a building's power usage.