On the Bahadur representation of sample quantiles for sequences of φ-mixing random variables |
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Authors: | Pranab Kumar Sen |
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Institution: | Department of Biostatistics, University of North Carolina, Chapel Hill, North Carolina USA |
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Abstract: | The object of the present investigation is to show that the elegant asymptotic almost-sure representation of a sample quantile for independent and identically distributed random variables, established by Bahadur 1] holds for a stationary sequence of φ-mixing random variables. Two different orders of the remainder term, under different φ-mixing conditions, are obtained and used for proving two functional central limit theorems for sample quantiles. It is also shown that the law of iterated logarithm holds for quantiles in stationary φ-mixing processes. |
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Keywords: | 60F05 60F15 |
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