Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1155831 | Stochastic Processes and their Applications | 2012 | 33 Pages |
Abstract
Assuming that {(Un,Vn)}{(Un,Vn)} is a sequence of càdlàg processes converging in distribution to (U,V)(U,V) in the Skorohod topology, conditions are given under which {∬fn(β,u,v)dUndVn}{∬fn(β,u,v)dUndVn} converges weakly to ∬f(β,x,y)dUdV∬f(β,x,y)dUdV in the space C(R)C(R), where fn(β,u,v)fn(β,u,v) is a sequence of “smooth” functions converging to f(β,u,v)f(β,u,v). Integrals of this form arise as the objective function for inference about a parameter ββ in a stochastic model. Convergence of these integrals play a key role in describing the asymptotics of the estimator of ββ which optimizes the objective function. We illustrate this with a moving average process.
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Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Richard A. Davis, Li Song,