Second Order Expansions for Sample Median with Random Sample Size

05/19/2019

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by   Gerd Christoph, et al.

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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.