PL EN


2011 | 876 | 105-120
Article title

Regresja wektorów losowych dla wielowymiarowego rozkładu t-Studenta

Authors
Title variants
EN
REGRESSION OF RANDOM VECTORS FOR MULTIVARIATE t-STUDENT DISTRIBUTION
Languages of publication
PL
Abstracts
EN
The paper examines the concept of „conditional expected value”, which is of great importance in modern finance. The considerations are carried out on a five dimensional random vector with multivariate t-Student distribution. In the first part we construct a distribution of its coordinates in a 2:3 ratio (i.e., the vectors are two-and three-dimensional, respectively) in order to find an effective two-dimensional vector regression function in relation to the three-dimensional vector. To that end, the probability density distribution of the boundary three-dimensional vector is determined (by calculating the appropriate double integral), and then the conditional probability density distribution of two-dimensional vector was used to produce the three-dimensional vector. The second part of the paper discusses the reasoning presented in the first part and then generalises it for a random vector of any size that will remain applicable provided that it is a multi-dimensional random vectors with t-Student distribution. The results (the general form of the regression function) are illustrated with a specific quantitative example that maintains a „hyperplane” regression.
Contributors
author
References
Document Type
Publication order reference
Identifiers
YADDA identifier
bwmeta1.element.desklight-76419029-869d-408e-8436-a69a39b10751
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