Self-normalized moderate deviations and lils
نویسندگان
چکیده
منابع مشابه
Self-normalized Moderate Deviations and Lils
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.
متن کاملCramér 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)).
متن کاملSelf-normalized Cramér type Moderate Deviations for the Maximum of Sums
Let X1, X2, . . . be independent random variables with zero means and finite variances, and let Sn = ∑n i=1Xi and V 2 n = ∑n i=1X 2 i . A Cramér type moderate deviation for the maximum of the self-normalized sums max1≤k≤n Sk/Vn is obtained. In particular, for identically distributed X1, X2, · · · , it is proved that P(max1≤k≤n Sk ≥ xVn)/(1 − Φ(x)) → 2 uniformly for 0 < x ≤ o(n1/6) under the opt...
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We introduce a family of convex (concave) functions called sup (inf) of powers, which are used as generator functions for a special type of quasi-arithmetic means. Using these means we generalize the large deviation result that was obtained in the homogeneous case by Shao [14] on selfnormalized statistics. Furthermore, in the homogenous case, we derive the Bahadur exact slope for tests using se...
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We prove that the Moderate Deviation Principle (MDP) holds for the trajectory of a locally square integrable martingale with bounded jumps as soon as its quadratic covariation, properly scaled, converges in probability at an exponential rate. A consequence of this MDP is the tightness of the method of bounded martingale diierences in the regime of moderate deviations.
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ژورنال
عنوان ژورنال: Stochastic Processes and their Applications
سال: 1998
ISSN: 0304-4149
DOI: 10.1016/s0304-4149(98)00007-6