Second Order Expansions for High-Dimension Low-Sample-Size Data Statistics in Random Setting

Gerd Christoph and Vladimir V. Ulyanov
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Gerd Christoph: Department of Mathematics, Otto-von-Guericke University Magdeburg, 39016 Magdeburg, Germany
Vladimir V. Ulyanov: Moscow Center for Fundamental and Applied Mathematics, Lomonosov Moscow State University, 119991 Moscow, Russia

Mathematics, 2020, vol. 8, issue 7, 1-28

Abstract: We consider high-dimension low-sample-size data taken from the standard multivariate normal distribution under assumption that dimension is a random variable. The second order Chebyshev–Edgeworth expansions for distributions of an angle between two sample observations and corresponding sample correlation coefficient are constructed with error bounds. Depending on the type of normalization, we get three different limit distributions: Normal, Student’s t -, or Laplace distributions. The paper continues studies of the authors on approximation of statistics for random size samples.

Keywords: second order expansions; high-dimensional; low sample size; random sample size; Laplace distribution; Student’s t-distribution (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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