Simple Estimators for Parametric Markovian Trend of Ergodic Processes Based on Sampled Data
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- Masuda Hiroki
- Graduate School of Mathematics, Kyushu University
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説明
Let X be a stochastic process obeying a stochastic differential equation of the form dXt = b(Xt, θ)dt + dYt, where Y is an adapted driving process possibly depending on X’s past history, and θ ∈ Θ ⊂ Rp is an unknown parameter. We consider estimation of θ when X is discretely observed at possibly non-equidistant time-points (tni)ni=0. We suppose hn := max1 ≤ i ≤ n(tni − tni − 1) → 0 and tnn → ∞ as n → ∞: the data becomes more high-frequency as its size increases. Under some regularity conditions including the ergodicity of X, we obtain √nhn-consistency of trajectory-fitting estimate as well as least-squares estimate, without identifying Y. Also shown is that some additional conditions, which requires Y's structure to some extent, lead to asymptotic normality. In particular, a Wiener-Poisson-driven setup is discussed as an important special case.
収録刊行物
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- JOURNAL OF THE JAPAN STATISTICAL SOCIETY
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JOURNAL OF THE JAPAN STATISTICAL SOCIETY 35 (2), 147-170, 2005
日本統計学会
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詳細情報 詳細情報について
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- CRID
- 1390001205287782400
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- NII論文ID
- 110003495321
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- NII書誌ID
- AA1105098X
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- ISSN
- 13486365
- 18822754
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- HANDLE
- 2324/11849
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- NDL書誌ID
- 7966696
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- 本文言語コード
- en
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