Switching Nonparametric Regression Models and the Motorcycle Data revisited

TL;DR

This paper introduces a switching nonparametric regression model with an EM algorithm for estimating multiple unknown smooth functions in data where the response switches among unobserved states, demonstrated on motorcycle accident data.

Contribution

It develops a novel EM-based methodology for modeling data with unobserved switching states and provides standard errors for parameter estimates.

Findings

The method accurately estimates multiple smooth functions.

Simulation studies confirm good frequentist properties.

Application to motorcycle data reveals unobserved state switching.

Abstract

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.