Nonlinear profile monitoring with single index models. (23rd December 2020) - Iguchi, Takayuki; Barrientos, Andrés F.; Chicken, Eric; Sinha, Debajyoti
Abstract: We consider change‐point detection and estimation in sequences of functional observations. This setting often arises when the quality of a process is characterized by such observations, called profiles, and monitoring profiles for changes in structure can be used to ensure the stability of the process over time. We propose a nonparametric approach using a single index model (SIM), where instead of monitoring the profile itself for a change, we monitor an l 2 ‐based statistic on the coefficients generated by the SIM. Through simulation we show our novel method outperforms existing multivariate profile monitoring methods.