THESIS
2013
iv leaves, v-ix, 112 pages : illustrations ; 30 cm
Abstract
The main contribution of this dissertation is two-fold. First, we establish general
Cramér type moderate deviation theorems for a class of Studentized non-linear
statistics, including Student's t-statistic, Studentized U- and L-statistics as prototypical
examples, by developing a novel randomized concentration inequality.
As a direct consequence, a sharp moderate deviation for Studentized U-statistics
is obtained. Second, we study the asymptotic behaviors of the largest magnitude
of the off-diagonal entries of the sample correlation matrix, under the ultra-high
dimensional setting. In particular, we obtain necessary and sufficient conditions
for the law of large numbers, and also establish limiting distributions under
the same sufficient condition. The proofs are based on both...[
Read more ]
The main contribution of this dissertation is two-fold. First, we establish general
Cramér type moderate deviation theorems for a class of Studentized non-linear
statistics, including Student's t-statistic, Studentized U- and L-statistics as prototypical
examples, by developing a novel randomized concentration inequality.
As a direct consequence, a sharp moderate deviation for Studentized U-statistics
is obtained. Second, we study the asymptotic behaviors of the largest magnitude
of the off-diagonal entries of the sample correlation matrix, under the ultra-high
dimensional setting. In particular, we obtain necessary and sufficient conditions
for the law of large numbers, and also establish limiting distributions under
the same sufficient condition. The proofs are based on both classical and self-normalized
moderate deviations, the Stein-Chen method and the aforementioned
randomized concentration inequality.
Post a Comment