Self normalized central limit theorem for some mixing processes.

Summary We prove a self normalized central limit theorem for a new mixing class of processes introduced in Kacem et al. (2013). This class is larger than the classical strongly mixing processes and thus our result is more general than Peligrad and Shao's (1995) and Shi's (2000) ones. The fact that some conditionally independent processes satisfy this kind of mixing properties motivated our study. We investigate the weak consistency as well as the asymptotic normality of the estimator of the variance that we propose.