TY - CHAP

T1 - Why student distributions? Why matern’s covariance model? a symmetry-based explanation

AU - Schön, Stephen

AU - Kermarrec, Gael

AU - Kargoll, Boris

AU - Neumann, Ingo

AU - Kosheleva, Olga

AU - Kreinovich, Vladik

N1 - Funding information: Acknowledgments. This work was performed when Olga Kosheleva and Vladik Kreinovich were visiting researchers with the Geodetic Institute of the Leibniz University of Hannover, a visit supported by the German Science Foundation. This work was also supported in part by NSF grant HRD-1242122.

PY - 2017/12/20

Y1 - 2017/12/20

N2 - In this paper, we show that empirical successes of Student distribution and of Matern’s covariance models can be indirectly explained by a natural requirement of scale invariance – that fundamental laws should not depend on the choice of physical units. Namely, while neither the Student distributions nor Matern’s covariance models are themselves scale-invariant, they are the only one which can be obtained by applying a scale-invariant combination function to scale-invariant functions.

AB - In this paper, we show that empirical successes of Student distribution and of Matern’s covariance models can be indirectly explained by a natural requirement of scale invariance – that fundamental laws should not depend on the choice of physical units. Namely, while neither the Student distributions nor Matern’s covariance models are themselves scale-invariant, they are the only one which can be obtained by applying a scale-invariant combination function to scale-invariant functions.

UR - http://www.scopus.com/inward/record.url?scp=85038850900&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-73150-6_21

DO - 10.1007/978-3-319-73150-6_21

M3 - Contribution to book/anthology

AN - SCOPUS:85038850900

T3 - Studies in Computational Intelligence

SP - 266

EP - 275

BT - Econometrics for Financial Applications

PB - Springer Verlag

ER -