TY - JOUR
T1 - Dvoretzky Type Theorems for Subgaussian Coordinate Projections
AU - Mendelson, Shahar
N1 - Publisher Copyright:
© 2015, Springer Science+Business Media New York.
PY - 2016/12/1
Y1 - 2016/12/1
N2 - Given a class of functions F on a probability space (Ω , μ) , we study the structure of a typical coordinate projection of the class, defined by {(f(Xi))i=1N:f∈F}, where X1, … , XN are independent, selected according to μ. We show that when F is a subgaussian class, a typical coordinate projection satisfies a Dvoretzky type theorem.
AB - Given a class of functions F on a probability space (Ω , μ) , we study the structure of a typical coordinate projection of the class, defined by {(f(Xi))i=1N:f∈F}, where X1, … , XN are independent, selected according to μ. We show that when F is a subgaussian class, a typical coordinate projection satisfies a Dvoretzky type theorem.
KW - Dvoretzky type theorems
KW - Empirical processes
KW - Subgaussian classes
UR - http://www.scopus.com/inward/record.url?scp=84933056699&partnerID=8YFLogxK
U2 - 10.1007/s10959-015-0624-x
DO - 10.1007/s10959-015-0624-x
M3 - Article
SN - 0894-9840
VL - 29
SP - 1644
EP - 1660
JO - Journal of Theoretical Probability
JF - Journal of Theoretical Probability
IS - 4
ER -