Some central limit theorems for ?∞-valued semimartingales and their applications |
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Authors: | Yoichi Nishiyama |
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Institution: | (1) The Institute of Statistical Mathematics, 4-6-7 Minami-Azabu, Minato-ku, Tokyo 106, Japan (e-mail: nisiyama@ism.ac.jp), JP |
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Abstract: | Summary. This paper is devoted to the generalization of central limit theorems for empirical processes to several types of ℓ∞(Ψ)-valued continuous-time stochastic processes t⇝X
t
n
=(X
t
n
,ψ|ψ∈Ψ), where Ψ is a non-empty set. We deal with three kinds of situations as follows. Each coordinate process t⇝X
t
n
,ψ is: (i) a general semimartingale; (ii) a stochastic integral of a predictable function with respect to an integer-valued
random measure; (iii) a continuous local martingale. Some applications to statistical inference problems are also presented.
We prove the functional asymptotic normality of generalized Nelson-Aalen's estimator in the multiplicative intensity model
for marked point processes. Its asymptotic efficiency in the sense of convolution theorem is also shown. The asymptotic behavior
of log-likelihood ratio random fields of certain continuous semimartingales is derived.
Received: 6 May 1996 / In revised form: 4 February 1997 |
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Keywords: | Mathematics Subject Classification (1991): 60F05 60F17 62E20 |
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