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Approximate ML and REML estimation for regression models with spatial or time series AR(1) noise

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  • Reinsel, Gregory C.
  • Cheang, Wai-Kwong

Abstract

This paper considers maximum likelihood (ML) and restricted maximum likelihood (REML) estimation of regression models with two-dimensional spatial or one-dimensional time series autoregressive AR(1) noise. Although the exact ML and REML procedures are described, the aim is to develop and present a simple estimation procedure that provides very accurate approximations to the ML and REML estimators and is computationally convenient. An approximation for the bias of the ML estimator of the AR parameters is also investigated. Simulation results are provided to assess the accuracy of our approximations.

Suggested Citation

  • Reinsel, Gregory C. & Cheang, Wai-Kwong, 2003. "Approximate ML and REML estimation for regression models with spatial or time series AR(1) noise," Statistics & Probability Letters, Elsevier, vol. 62(2), pages 123-135, April.
    • Handle: RePEc:eee:stapro:v:62:y:2003:i:2:p:123-135
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    References listed on IDEAS

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    1. Brent D. Burch & Ian R. Harris, 2001. "Closed-Form Approximations to the REML Estimator of a Variance Ratio (or Heritability) in a Mixed Linear Model," Biometrics, The International Biometric Society, vol. 57(4), pages 1148-1156, December.
    2. Pantula, Sastry G & Gonzalez-Farias, Graciela & Fuller, Wayne A, 1994. "A Comparison of Unit-Root Test Criteria," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(4), pages 449-459, October.
    3. Heon Jin Park & Wayne A. Fuller, 1995. "Alternative Estimators And Unit Root Tests For The Autoregressive Process," Journal of Time Series Analysis, Wiley Blackwell, vol. 16(4), pages 415-429, July.
    4. Cordeiro, Gauss M. & Klein, Ruben, 1994. "Bias correction in ARMA models," Statistics & Probability Letters, Elsevier, vol. 19(3), pages 169-176, February.
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