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Local Asymptotic Normality for Linear Homogeneous Difference Equations with Non-Gaussian Noise

Author

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  • Andrius Jankunas

    (Wayne State University)

Abstract

This paper considers the problem of estimation of drift parameter for linear homogeneous stochastic difference equations. The Local Asymptotic Normality (LAN) for the problem is proved. LAN implies the Hajek–Le Cam minimax lower bound. In particular, it is shown that the Fisher's information matrix for the problem can be expressed in terms of the stationary distribution of an auxiliary Markov chain on the projective space P(ℝd).

Suggested Citation

  • Andrius Jankunas, 1999. "Local Asymptotic Normality for Linear Homogeneous Difference Equations with Non-Gaussian Noise," Journal of Theoretical Probability, Springer, vol. 12(3), pages 675-697, July.
    • Handle: RePEc:spr:jotpro:v:12:y:1999:i:3:d:10.1023_a:1021623714825
    DOI: 10.1023/A:1021623714825
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    References listed on IDEAS

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    1. Jankunas, Andrius & Khasminskii, Rafail Z., 1997. "Estimation of parameters of linear homogeneous stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 72(2), pages 205-219, December.
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