Multiple Change Point Detection Method of Profile Data With False Discovery Rate Control

Multiple change point detection seeks to identify potential shifts in the data properties. While existing detection methods primarily focus on univariate and multivariate data, they often fall short in detecting variations in profile data, which represent the functional relationships between explanatory and response variables. This paper introduces a novel change point detection method tailored for profile data, employing a smooth profile decomposition (SPD) strategy that accommodates arbitrary designs and heteroscedasticity. This approach facilitates a comprehensive representation of both overall trends and fluctuations within the profiles. Furthermore, we propose an order-splitting screening estimator (OSE) to construct a detection statistic, allowing for precise estimation of change points while ensuring a significant theoretical guarantee regarding the false discovery rate (FDR). We validate the performance and robustness of the proposed method through numerical experiments and a real case study involving wind turbines.