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B1574
**Title: **A Cramer moderate deviation theorem for general self-normalized sums
**Authors: **Jiasheng Shi - The Chinese University of Hong Kong (Hong Kong) **[presenting]**

Qi-Man Shao - The Chinese University of Hong Kong (Hong Kong)

Lan Gao - The Chinese University of Hong Kong (Hong Kong)

**Abstract: **Asymptotic theory for self-normalized sums has been well studied in the past two decades. The aim is to focus on a general self-normalized sums $\frac{\sum_{i=1}^{n}X_i}{\sqrt{\sum_{i=1}^nY_i^2}}$, where $(X_i,Y_i)$, for $i$ from 1 to $n$, are independent random vectors. The Cramer type moderate deviation theorem is obtained under optimal moment condition. Applications to self-normalized dependent random variables, as in the case of longitudinal data and beta mixing time series will also be discussed.

Qi-Man Shao - The Chinese University of Hong Kong (Hong Kong)

Lan Gao - The Chinese University of Hong Kong (Hong Kong)