Self-normalized Moderate Deviations and Lils
نویسندگان
چکیده
Let fXn;n 1g be i.i.d. R d-valued random variables. We prove Partial Moderate Deviation Principles for self-normalized partial sums subject to minimal moment assumptions. Applications to the self-normalized law of the iterated logarithm are also discussed.
منابع مشابه
Cramér Type Moderate deviations for the Maximum of Self-normalized Sums
Let {X ,X i , i ≥ 1} be i.i.d. random variables, Sk be the partial sum and V 2 n = ∑n i=1 X 2 i . Assume that E(X ) = 0 and E(X )<∞. In this paper we discuss the moderate deviations of the maximum of the self-normalized sums. In particular, we prove that P(max1≤k≤n Sk ≥ x Vn)/(1−Φ(x))→ 2 uniformly in x ∈ [0, o(n)).
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