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This paper presents a data-driven prognostic framework for rolling-element bearings (REBs). This framework infers a bearing's health index by defining a degree-of-defectiveness (DD) metric in the frequency domain of bearing raw signal, named DD-based health index (DDHI). Then, we systematically apply least-square support vector machines (LSSVMs) in the forms of Bayesian inference-aided one-class LSSVM (Bayesian-OCLSSVM) for anomaly detection in order to define the time-to-start (TTS) point of RUL prediction and the recurrent least-square support vector regression (Recurrent-LSSVR) model for predicting future values of DDHI for calculating the RUL. In addition, this paper addresses several pertinent challenges, such as failure threshold determination during anomaly detection and RUL estimation, by developing adaptive thresholds. We conduct extensive experiments on publicly available two benchmark datasets using a run-to-failure experiment. The results demonstrate the efficacy of the proposed framework compared to state-of-the-art methods in terms of the accuracy and convergence of the RUL estimation of bearings. [ABSTRACT FROM AUTHOR]