Second Order Expansions for Sample Median with Random Sample Size

2019/05/19 by Gerd Christoph, Christoph, Gerd, Vladimir V. Ulyanov +3
Mathematics · #60E05 (Secondary) #62E17 (Primary) 62H10 #FOS: Mathematics #Statistics Theory (math.ST) #math.ST #msc:60E05 #msc:62E17 #msc:62H10 #stat.TH

paper · pdf · doi:10.48550/arxiv.1905.07765

23 pages

arxiv created 2020/06/24 · arxiv updated 2020/06/25

Abstract

In practice, we often encounter situations where a sample size is not defined in advance and can be a random value. The randomness of the sample size crucially changes the asymptotic properties of the underlying statistic. In the present paper second order Chebyshev--Edgeworth and Cornish--Fisher expansions based of Student's t- and Laplace distributions and their quantiles are derived for sample median with random sample size of a special kind.

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