Speaker
Adam Kashlak
(Cambridge Centre for Analysis, University of Cambridge)
Description
In the modern era of high and infinite dimensional data, classical statistical
methodology is often rendered inefficient and ineffective when confronted
with such big data problems as arise in genomics, medical imaging, speech
analysis, and many other areas of research. Many problems manifest when
the practitioner is required to take into account the covariance structure
of the data during his or her analysis, which takes on the form of either a
high dimensional low rank matrix or a finite dimensional representation of
an infinite dimensional operator acting on some underlying function space.
Thus, we propose using tools from the concentration of measure literature
to construct rigorous descriptive and inferential statistical methodology for
covariance matrices and operators. A variety of concentration inequalities are
considered, which allow for the construction of nonasymptotic dimension-free
confidence sets for the unknown matrices and operators. Given such confidence
sets a wide range of estimation and inferential procedures can be and are
subsequently developed.
Primary author
Adam Kashlak
(Cambridge Centre for Analysis, University of Cambridge)
