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Self-normalized deviation inequalities with application to t-statistic

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  • Fan, Xiequan

Abstract

Let (ξi)i≥1 be a sequence of independent and symmetric random variables. We obtain some upper bounds on tail probabilities of self-normalized deviations P(max1≤k≤n∑i=1kξi/(∑i=1n∣ξi∣β)1/β≥x) for x>0 and β>1. Our bound is the best that can be obtained from the Bernstein inequality under the present assumption. An application to Student’s t-statistic is also given.

Suggested Citation

  • Fan, Xiequan, 2017. "Self-normalized deviation inequalities with application to t-statistic," Statistics & Probability Letters, Elsevier, vol. 127(C), pages 158-164.
    • Handle: RePEc:eee:stapro:v:127:y:2017:i:c:p:158-164
    DOI: 10.1016/j.spl.2017.04.006
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    References listed on IDEAS

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    1. Grama, Ion & Haeusler, Erich, 2000. "Large deviations for martingales via Cramér's method," Stochastic Processes and their Applications, Elsevier, vol. 85(2), pages 279-293, February.
    2. Fan, Xiequan & Grama, Ion & Liu, Quansheng, 2012. "Hoeffding’s inequality for supermartingales," Stochastic Processes and their Applications, Elsevier, vol. 122(10), pages 3545-3559.
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