George Roussas
Division of Statistics
University of California, Davis
Asymptotic Behavior and Exponential Approximation
of the Likelihood Function
In this presentation,we consider the likelihood function, based on a random
number of observations coming from a general discrete time parameter
stochastic process, and study its asymptotic behavior. Specifically, its
local asymptotic expansion in the probability sense is obtained, as well as
its asymptotic distribution, and local exponential approximation. Results
are obtained under regular assumptions, which lead to asymptotic
normality, and under non-standard assumptions, which lead to mixtures of
normal distributions. Contiguity tools are instrumental in the derivations.
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