Strong Moderate Deviation Theorems


Inglot, Tadeusz and Kallenberg, Wilbert C.M. and Ledwina, Teresa (1992) Strong Moderate Deviation Theorems. Annals of Probability, 20 (2). pp. 987-1003. ISSN 0091-1798

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Abstract:Strong moderate deviation theorems are concerned with relative errors in the tails caused by replacing the exact distribution function by its limiting distribution function. A new approach for deriving such theorems is presented using strong approximation inequalities. In this way a strong moderate deviation theorem is obtained for statistics of the form $T(\alpha_n)$, where $T$ is a sublinear functional and $\alpha_n$ is the empirical process. The basic theorem is also applied on linear combinations of order statistics, leading to a substantial improvement of previous results.
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Copyright:© 1992 Institute of Mathematical Statistics
Electrical Engineering, Mathematics and Computer Science (EEMCS)
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