Self-normalized deviation inequalities with application to t-statistic

Xiequan Fan

Statistics & Probability Letters, 2017, vol. 127, issue C, 158-164

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.

Keywords: Self-normalized deviations; Student’s t-statistic; Exponential inequalities (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1016/j.spl.2017.04.006

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