On the Rate of Convergence in Normal Approximation and Large Deviation Probabilities for a Class of Statistics
Document Type
Article
Publication Date
7-11-2011
Identifier/URL
40902518 (Pure)
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Abstract
A new class of statistics is introduced to include,as special cases, unsigned linear rank statistics, signed linearrank statistics, linear combinations of functions of orderstatistics, linear functions of concomitants of order statisticsand a rank combinatorial statistic. For this class, the rate ofconvergence to normality and Cramér-type large deviationprobabilities are investigated. Under the assumption that the underlyingobservations are only independent, it is shown that this rate isO(N−δ/2logN) if the first derivative of the score-generatingfunction φ satisfies a Lipschitz condition of order δ,0<δ≤1, that it is O(N−1/2) if φ′′satisfies a Lipschitz condition of order δ≥12, andthat Cramér's large deviation theorem holds in the optimal range0
Repository Citation
Purif, M. L.,
& Seoh, M.
(2011). On the Rate of Convergence in Normal Approximation and Large Deviation Probabilities for a Class of Statistics. Probability Theory and Extreme Value Theory, 2, 205-220.
https://corescholar.libraries.wright.edu/math/501
Comments
Publisher Copyright: © VSP 2003.