Self-Normalized Moderate Deviations for Degenerate U -Statistics

In this paper, we study self-normalized moderate deviations for degenerate -statistics of order 2. Let {Xi,i≥1} be i.i.d. random variables and consider symmetric and degenerate kernel functions in the form h(x,y)=∑l=1∞λlgl(x)gl(y), where λl>0, Egl(X1)=0, and gl(X1) is in the domain of attraction of a normal law for all l≥1. Under the condition ∑l=1∞λl