Simple Estimators for Parametric Markovian Trend of Ergodic Processes Based on Sampled Data

• Masuda Hiroki

  Graduate School of Mathematics, Kyushu University

Abstract

Let X be a stochastic process obeying a stochastic differential equation of the form dX_t = b(X_t, θ)dt + dY_t, where Y is an adapted driving process possibly depending on X’s past history, and θ ∈ Θ ⊂ R^p is an unknown parameter. We consider estimation of θ when X is discretely observed at possibly non-equidistant time-points (tⁿ_i)ⁿ_i=0. We suppose h_n := max_{1 ≤ i ≤ n}(tⁿ_i − tⁿ_{i − 1}) → 0 and tⁿ_n → ∞ as n → ∞: the data becomes more high-frequency as its size increases. Under some regularity conditions including the ergodicity of X, we obtain √nh_n-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.

Journal

• JOURNAL OF THE JAPAN STATISTICAL SOCIETY

  JOURNAL OF THE JAPAN STATISTICAL SOCIETY 35 (2), 147-170, 2005

  THE JAPAN STATISTICAL SOCIETY

Keywords

• discrete sampling
• parametric estimation
• stochastic differential equation
• trajectory-fitting

Details

• CRID: 1390001205287782400
• NII Article ID: 110003495321
• NII Book ID: AA1105098X
• DOI: 10.14490/jjss.35.147
• ISSN: 13486365
• ISSN: 18822754
• HANDLE: 2324/11849
• NDL BIB ID: 7966696
• Web Site: https://ndlsearch.ndl.go.jp/books/R000000004-I7966696
• Web Site: https://www.jstage.jst.go.jp/article/jjss/35/2/35_2_147/_pdf
• Text Lang: en
• Data Source:
  • JaLC
  • IRDB
  • NDL
  • Crossref
  • CiNii Articles
  • KAKEN
• Abstract License Flag: Disallowed