Bootstrap confidence regions based on the Mahalanobis depth measure of two-dimensional samples

• Authors: Kobylińska, Małgorzata , Wagner, Wiesław

Title variants

EN

Bootstrapowe obszary ufności oparte na zanurzaniu Mahalanobisa dla prób dwuwymiarowych

Abstracts

EN

Construction of confidence regions for multi-dimensional samples is usually performed with a known stochastic distribution of a random vector in question. However, for multidimensional studies of socio-economic phenomena, such an assumption is difficult to make. Bootstrap methods can be helpful. The main problem with its application is the aligning of respective vectors. To this end, depth measures are used which express the vector distance from the central vector system cluster. Among many such depth measures, the Mahalanobis measure is one of the easiest from a numerical point of view. This paper presents a bootstrap region creation algorithm. It was illustrated for a two-dimensional sample.

PL

W pracy przedstawiony został algorytm tworzenia obszarów bootstrapowych. Do konstrukcji tych obszarów wykorzystano miary zanurzania obserwacji w próbie. Konstrukcję zaprezentowano dla przypadku dwuwymiarowego.

Keywords

EN

depth measure; measure of depth by Mahalanobis; bootstrap methods

• Publisher: Uniwersytet Łódzki. Wydawnictwo Uniwersytetu Łódzkiego
• Journal: Acta Universitatis Lodziensis. Folia Oeconomica
• Year: 2008
• Volume: 216

Dates

published

2008

Contributors

author

Kobylińska, Małgorzata

author

Wagner, Wiesław

other

University of Warmia-and-Mazury in Olsztyn

other

Higher School of Information Technology and Management in Rzeszów

Identifiers

URI

http://hdl.handle.net/11089/16174