The perfect marriage and much more : Combining dimension reduction, distance measures and covariance
Research output: Journal Publications and Reviews (RGC: 21, 22, 62) › 21_Publication in refereed journal › peer-review
Author(s)
Related Research Unit(s)
Detail(s)
Original language | English |
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Article number | 120938 |
Journal / Publication | Physica A: Statistical Mechanics and its Applications |
Volume | 536 |
Online published | 8 Jul 2019 |
Publication status | Published - 15 Dec 2019 |
Link(s)
Abstract
We develop a novel methodology based on the marriage between the Bhattacharyya distance, a measure of similarity across distributions of random variables, and the Johnson–Lindenstrauss Lemma, a technique for dimension reduction. The resulting technique is a simple yet powerful tool that allows comparisons between data-sets representing any two distributions. The degree to which different entities, (markets, universities, hospitals, cities, groups of securities, etc.), have different distance measures of their corresponding distributions tells us the extent to which they are different, aiding participants looking for diversification or looking for more of the same thing. We demonstrate a relationship between covariance and distance measures based on a generic extension of Stein's Lemma. We consider an asset pricing application and then briefly discuss how this methodology lends itself to numerous market–structure studies and even applications outside the realm of finance / social sciences by illustrating a biological application. We provide numerical illustrations using security prices, volumes and volatilities of both these variables from six different countries.
Research Area(s)
- Bhattacharyya, Covariance, Dimension reduction, Distance measure, Distribution, Johnson–Lindenstrauss, Uncertainty
Bibliographic Note
Full text of this publication does not contain sufficient affiliation information. With consent from the author(s) concerned, the Research Unit(s) information for this record is based on the existing academic department affiliation of the author(s).
Citation Format(s)
The perfect marriage and much more: Combining dimension reduction, distance measures and covariance. / Kashyap, Ravi.
In: Physica A: Statistical Mechanics and its Applications, Vol. 536, 120938, 15.12.2019.
In: Physica A: Statistical Mechanics and its Applications, Vol. 536, 120938, 15.12.2019.
Research output: Journal Publications and Reviews (RGC: 21, 22, 62) › 21_Publication in refereed journal › peer-review