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Weighted empirical adaptive variance estimators for correlated data regression

Author

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  • T. Lumley
  • P. Heagerty

Abstract

Estimating equations based on marginal generalized linear models are useful for regression modelling of correlated data, but inference and testing require reliable estimates of standard errors. We introduce a class of variance estimators based on the weighted empirical variance of the estimating functions and show that an adaptive choice of weights allows reliable estimation both asymptotically and by simulation in finite samples. Connections with previous bootstrap and jackknife methods are explored. The effect of reliable variance estimation is illustrated in data on health effects of air pollution in King County, Washington.

Suggested Citation

  • T. Lumley & P. Heagerty, 1999. "Weighted empirical adaptive variance estimators for correlated data regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(2), pages 459-477, April.
    • Handle: RePEc:bla:jorssb:v:61:y:1999:i:2:p:459-477
    DOI: 10.1111/1467-9868.00187
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    Cited by:

    1. Liu, Haibin & Davidson, Rachel A. & Apanasovich, Tatiyana V., 2008. "Spatial generalized linear mixed models of electric power outages due to hurricanes and ice storms," Reliability Engineering and System Safety, Elsevier, vol. 93(6), pages 897-912.
    2. Wu, Rongning, 2012. "On variance estimation in a negative binomial time series regression model," Journal of Multivariate Analysis, Elsevier, vol. 112(C), pages 145-155.
    3. Kostyrka, Andreï & Malakhov, Dmitry, 2021. "Was there ever a shift: Empirical analysis of structural-shift tests for return volatility," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 61, pages 110-139.
    4. Zeileis, Achim, 2006. "Implementing a class of structural change tests: An econometric computing approach," Computational Statistics & Data Analysis, Elsevier, vol. 50(11), pages 2987-3008, July.
    5. Jens J. Krüger, 2016. "Radar scanning the world production frontier," Journal of Productivity Analysis, Springer, vol. 46(1), pages 1-13, August.
    6. Nicole Mayer-Hamblett & Steve Self, 2001. "A Regression Modeling Approach for Describing Patterns of HIV Genetic Variation," Biometrics, The International Biometric Society, vol. 57(2), pages 449-460, June.
    7. Zeileis, Achim, 2004. "Econometric Computing with HC and HAC Covariance Matrix Estimators," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 11(i10).
    8. Ding, Peng, 2021. "The Frisch–Waugh–Lovell theorem for standard errors," Statistics & Probability Letters, Elsevier, vol. 168(C).
    9. Fruehwirt, Wolfgang & Hochfilzer, Leonhard & Weydemann, Leonard & Roberts, Stephen, 2021. "Cumulation, crash, coherency: A cryptocurrency bubble wavelet analysis," Finance Research Letters, Elsevier, vol. 40(C).
    10. repec:jss:jstsof:11:i10 is not listed on IDEAS
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    12. Francesca Dominici & Lianne Sheppard & Merlise Clyde, 2003. "Health Effects of Air Pollution: A Statistical Review," International Statistical Review, International Statistical Institute, vol. 71(2), pages 243-276, August.
    13. Peng Ding, 2020. "The Frisch--Waugh--Lovell Theorem for Standard Errors," Papers 2009.06621, arXiv.org.
    14. Stupfler, Gilles & Yang, Fan, 2018. "Analyzing And Predicting Cat Bond Premiums: A Financial Loss Premium Principle And Extreme Value Modeling," ASTIN Bulletin, Cambridge University Press, vol. 48(1), pages 375-411, January.
    15. Alonso Cifuentes, Julio César & Jaramillo Flechas, Luis Eduardo, 2019. "Descomponiendo el Efecto del Gasto Público en la Tasa de Cambio Real: Una Aproximación al Caso Colombiano || Decomposing the Effect of Public Spending on the Real Exchange Rate: An Approximation to th," Revista de Métodos Cuantitativos para la Economía y la Empresa = Journal of Quantitative Methods for Economics and Business Administration, Universidad Pablo de Olavide, Department of Quantitative Methods for Economics and Business Administration, vol. 27(1), pages 91-114, June.
    16. Zeileis, Achim, 2006. "Object-oriented Computation of Sandwich Estimators," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 16(i09).
    17. Javier Contreras-Reyes & Wilfredo Palma, 2013. "Statistical analysis of autoregressive fractionally integrated moving average models in R," Computational Statistics, Springer, vol. 28(5), pages 2309-2331, October.
    18. Lucio Capitani & Leo Pasquazzi, 2015. "Inference for performance measures for financial assets," METRON, Springer;Sapienza Università di Roma, vol. 73(1), pages 73-98, April.

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