Statistica Sinica 23 (2013), 1673-1696
A NEW CONDITION FOR
THE INVARIANCE PRINCIPLE
FOR STATIONARY RANDOM FIELDS
Yizao Wang and Michael Woodroofe
University of Cincinnati and
University of Michigan
Abstract: We establish a central limit theorem and
an invariance principle for stationary random fields, with
projective-type conditions. Our result is obtained via an
-dependent approximation method. As applications, we establish
invariance principles for orthomartingales and functionals of linear
random fields.
Key words and
phrases: Central limit theorem, invariance principle, linear random
field, -dependent approximation, orthomartingale.