The disclosed embodiments provide a system that detects sensor anomalies in a univariate time-series signal. During a surveillance mode, the system receives the univariate time-series signal from a sensor in a monitored system. Next, the system performs a staggered-sampling operation on the univariate time-series signal to produce N sub-sampled time-series signals, wherein the staggered-sampling operation allocates consecutive samples from the univariate time-series signal to the N sub-sampled time-series signals in a round-robin ordering. The system then uses a trained inferential model to generate estimated values for the N sub-sampled time-series signals based on cross-correlations with other sub-sampled time-series signals. Next, the system performs an anomaly detection operation to detect incipient sensor anomalies in the univariate time-series signal based on differences between actual values and the estimated values for the N sub-sampled time-series signals. Whenever an incipient sensor anomaly is detected, the system generates a notification.