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Inference for Shot Noise

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Abstract

This paper studies estimation issues for Poisson shot noise models from a data history observed on a discrete-time lattice. Optimal estimating function methods in the sense of Godambe (1985) are developed for the case when the impulse response function of the shot process is interval similar; moment methods are explored for compactly supported impulse responses. Asymptotic normality of the proposed estimates is established and the limiting covariance of the estimates is derived. Applications of the methods to several parametric shot function types are presented.

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References

  • S. Bevan R. Kullberg J. Rice (1979) ArticleTitleAn analysis of membrane noise Ann Stat 7 237–257

    Google Scholar 

  • P.J. Brockwell R.A. Davis (1991) Time Series: Theory and Methods EditionNumber2 Springer–Verlag New York

    Google Scholar 

  • R.A. Doney G.L. O’Brien (1991) ArticleTitleLoud shot noise Ann. Appl. Probab 1 88–103 Occurrence Handle92e:60171

    MathSciNet  Google Scholar 

  • V.P. Godambe (1985) ArticleTitleThe foundations of finite estimation in stochastic process Biometrika 72 419–428 Occurrence Handle10.2307/2336094 Occurrence Handle0584.62135 Occurrence Handle86k:62157

    Article  MATH  MathSciNet  Google Scholar 

  • C.C. Heyde (1997) Quasilikelihood and its Application A General Approach to Parameter Estimation Springer New York

    Google Scholar 

  • P. Hall C.C. Heyde (1980) Martingale Limit Theory and its Application Academic Press New York

    Google Scholar 

  • P. Lauger (1975) ArticleTitleShot noise in ion channels, Biochem Biophys. Acta. 413 1–10

    Google Scholar 

  • R.B. Lund R. Butler R.L. Paige (1999) ArticleTitlePrediction of shot noise J. Appl. Probab. 36 374–388 Occurrence Handle10.1239/jap/1032374459 Occurrence Handle2000g:60069

    Article  MathSciNet  Google Scholar 

  • W.P. McCormick (1998) ArticleTitleExtremes for shot noise processes with heavy tailed amplitudes J. Appl. Probab. 34 643–656 Occurrence Handle10.2307/3215091 Occurrence Handle98k:60082

    Article  MathSciNet  Google Scholar 

  • J. Rice (1977) ArticleTitleOn generalized shot noise Adv. Appl. Probab. 9 553–565 Occurrence Handle10.2307/1426114 Occurrence Handle0379.60052 Occurrence Handle58 #3133

    Article  MATH  MathSciNet  Google Scholar 

  • M. Sørensen (2000) ArticleTitlePrediction–based estimating equations Economet. J. 3 123–147 Occurrence Handle10.1111/1368-423X.00042 Occurrence Handle0998.62071

    Article  MATH  Google Scholar 

  • G. Samorodnitsky (1997) A class of shot–noise models for financial applications C.C. Heyde V. Prohorov Yu R. Pyke S.T. Rachev (Eds) Athens Conference on Applied Probability and Time Series, Volume I. Springer Berlin 332–353

    Google Scholar 

  • G. Samorodnitsky (1998) Tail behavior of some shot noise processes R.J. Adler R.E. Feldman M.S. Taqqu (Eds) A Practical Guide to Heavy Tails: Statistical Techniques and Applications. Birkhäuser Basel 473–478

    Google Scholar 

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Authors and Affiliations

  1. Department of Biostatistics and Computational Biology, The University of Rochester, Rochester, NY, 14642, USA

    Yuanhui Xiao

  2. Department of Mathematical Sciences, Clemson University, O-106 Martin Hall, Box 340975, Clemson, SC, 29634-0975, USA

    Robert Lund

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  1. Yuanhui Xiao
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  2. Robert Lund
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Correspondence to Robert Lund.

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Xiao, Y., Lund, R. Inference for Shot Noise. Stat Infer Stoch Process 9, 77–96 (2006). https://doi.org/10.1007/s11203-004-5350-4

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  • DOI: https://doi.org/10.1007/s11203-004-5350-4

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