Perspective of Self-normalized Limit Theory

Limit theory plays an important role in probability and statistics. Classical limit theorems such as the law of large numbers , the central limit theorem and the Craḿer moderate deviation theorem, under deterministic standardization, have been well developed and understood. However, standardized coefficients in applications are more often random, or self-normalized. In this talk, we shall review recent developments of limit theory for self-normalized processes as well as applications to statistical inference.