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A stable estimator of the information matrix under EM for dependent data

Statistics and Computing volume 21, pages 83–91 (2011)Cite this article

Abstract

This article develops a new and stable estimator for information matrix when the EM algorithm is used in maximum likelihood estimation. This estimator is constructed using the smoothed individual complete-data scores that are readily available from running the EM algorithm. The method works for dependent data sets and when the expectation step is an irregular function of the conditioning parameters. In comparison to the approach of Louis (J. R. Stat. Soc., Ser. B 44:226–233, 1982), this new estimator is more stable and easier to implement. Both real and simulated data are used to demonstrate the use of this new estimator.

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References

  • Cappe, O., Moulines, E.: On the use of particle filtering for maximum likelihood parameter estimation. In: European Signal Processing Conference (EUSIPCO), Antalya, Turkey (2005)

  • Dempster, A.P., Laird, N.M., Rubin, D.B.: Maximum likelihood from incomplete data via the EM algorithm. J. Am. Stat. Assoc., Ser. B 39, 1–38 (1977)

    MATH  MathSciNet  Google Scholar 

  • Doucet, A., de Freitas, N., Gordon, N. (eds.): Sequential Monte Carlo Methods in Practice. Springer, Berlin (2001)

    MATH  Google Scholar 

  • Jamshidian, M., Jennrich, R.I.: Standard errors for EM estimation. J. R. Stat. Soc., Ser. B 62, 257–270 (2000)

    Article  MathSciNet  Google Scholar 

  • Kiefer, N.M., Vogelsang, T.J.: A new asymptotic theory for heteroskedasticity-autocorrelation robust tests. Econom. Theory 21, 1130–1164 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  • Louis, T.A.: Finding the observed information matrix when using the EM algorithm. J. R. Stat. Soc., Ser. B 44, 226–233 (1982)

    MATH  MathSciNet  Google Scholar 

  • Meilijson, I.: A fast improvement to the EM algorithm on its own terms. J. R. Stat. Soc., Ser. B 51, 127–138 (1989)

    MATH  MathSciNet  Google Scholar 

  • Meng, X.L., Rubin, D.B.: Using EM to obtain asymptotic variance-covariance matrices: the SEM algorithm. J. Am. Stat. Assoc. 86, 899–909 (1991)

    Article  Google Scholar 

  • Newey, W.K., West, K.D.: A simple, positive semi-definite, heteroskedasticity and autocorrelation consistent covariance matrix. Econometrica 55, 703–708 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  • Olsson, J., Cappe, R., Douc, R., Moulines, E.: Sequential Monte Carlo smoothing with application to parameter estimation in non-linear state space models. Bernoulli 14, 155–179 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  • Shumway, R.H., Stoffer, D.S.: An approach to time series smoothing and forecasting using the EM algorithm. J. Time Ser. Anal. 3, 253–264 (1982)

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. Risk Management Institute and Department of Finance, National University of Singapore, Singapore, Singapore

    Jin-Chuan Duan

  2. ESSEC Business School, Paris, France

    Andras Fulop

Authors
  1. Jin-Chuan Duan
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  2. Andras Fulop
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Corresponding author

Correspondence to Andras Fulop.

Additional information

A. Fulop is a research fellow at CREST.

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Duan, JC., Fulop, A. A stable estimator of the information matrix under EM for dependent data. Stat Comput 21, 83–91 (2011). https://doi.org/10.1007/s11222-009-9149-4

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  • DOI: https://doi.org/10.1007/s11222-009-9149-4

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