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

Abstract

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.

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