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Power electronics (PE) and high-frequency switching circuits are key to superior performance of electric vehicles. It is vital to monitor the condition of the PE components in real-time for safety and reliability. In this article, we propose two anomaly detection methods based on a combination of data preprocessing to suppress noise and outliers, multivariate regression models to predict signals of interest under nominal operation, and sequential analysis of residuals. In particular, the methods utilize median filtering to extract on-state medians in each switching cycle in nonlinear autoregressive exogenous neural network models or filtered on-state data in partial least squares-based models to represent the nominal circuit behavior. Optimal and approximate dynamic programming-based feature selection methods are developed to select the most informative signals or their transformations. Predictions from the learned models are used to generate the residuals for anomaly detection by Page's cumulative sum test. The proposed models and anomaly detection methods are validated on three accelerated aging experimental datasets, comprised of 60 power mosfet devices with low-frequency and high-frequency switching under disparate operating conditions. Due to the simplicity and efficiency of the data-driven anomaly detection schemes, the proposed methods can potentially be embedded in real-time digital platforms.