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

P. 214–218.

Ulyanov V. V., Christoph G.

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: Chebyshev–Edgeworth expansions, high-dimension, low-sample-size

Publication based on the results of: Uncertainty quantification in high-dimensional models (2020)

In book

Сборник материалов V-й Международной конференции по стохастическим методам: The 5th International Conference on Stochastic Methods (ICSM5). 23-27 November 2020, Russia, Moscow.

M.: RUDN, 2020.