Third-order asymptotic expansion of <Emphasis Type="Italic">M</Emphasis>-estimators for diffusion processes |
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Authors: | Yuji Sakamoto Nakahiro Yoshida |
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Institution: | (1) Graduate School of Human Development and Environment, Kobe University, 3-11 Tsurukabuto, Nada, Kobe 657-8501, Japan;(2) Graduate School of Mathematical Sciences, The University of Tokyo, Tokyo, Japan;(3) Japan Science and Technology Agency, Tokyo, Japan |
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Abstract: | For an unknown parameter in the drift function of a diffusion process, we consider an M-estimator based on continuously observed data, and obtain its distributional asymptotic expansion up to the third order.
Our setting covers the misspecified cases. To represent the coefficients in the asymptotic expansion, we derive some formulas
for asymptotic cumulants of stochastic integrals, which are widely applicable to many other problems. Furthermore, asymptotic
properties of cumulants of mixing processes will be also studied in a general setting. |
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Keywords: | Asymptotic expansion M-estimator Diffusion process |
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