Let X1,X2,... be a sequence of independent random variables (r.v.s) belonging to the domain of attraction of a normal or stable law. In this paper, we study moderate deviations for the self-normalized sum n X ∑^n_i...Let X1,X2,... be a sequence of independent random variables (r.v.s) belonging to the domain of attraction of a normal or stable law. In this paper, we study moderate deviations for the self-normalized sum n X ∑^n_i=1Xi/Vm,p ,where Vn,p (∑^n_i=1|Xi|p)^1/p (P 〉 1).Applications to the self-normalized law of the iteratedlogarithm, Studentized increments of partial sums, t-statistic, and weighted sum of independent and identically distributed (i.i.d.) r.v.s are considered.展开更多
基金supported by Hong Kong Research Grant Committee (Grant Nos.HKUST6019/10P and HKUST6019/12P)National Natural Science Foundation of China (Grant Nos. 10871146 and 11271286)the National University of Singapore (Grant No. R-155-000-106-112)
文摘Let X1,X2,... be a sequence of independent random variables (r.v.s) belonging to the domain of attraction of a normal or stable law. In this paper, we study moderate deviations for the self-normalized sum n X ∑^n_i=1Xi/Vm,p ,where Vn,p (∑^n_i=1|Xi|p)^1/p (P 〉 1).Applications to the self-normalized law of the iteratedlogarithm, Studentized increments of partial sums, t-statistic, and weighted sum of independent and identically distributed (i.i.d.) r.v.s are considered.