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Parameter Orthogonality and Bias Adjustment for Estimating Functions

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  • Bent Jørgensen
  • Sven Jesper Knudsen

Abstract

. We consider an extended notion of parameter orthogonality for estimating functions, called nuisance parameter insensitivity, which allows a unified treatment of nuisance parameters for a wide range of methods, including Liang and Zeger's generalized estimating equations. Nuisance parameter insensitivity has several important properties in common with conventional parameter orthogonality, such as the nuisance parameter causing no loss of efficiency for estimating the interest parameter, and a simplified estimation algorithm. We also consider bias adjustment for profile estimating functions, and apply the results to restricted maximum likelihood estimation of dispersion parameters in generalized estimating equations.

Suggested Citation

  • Bent Jørgensen & Sven Jesper Knudsen, 2004. "Parameter Orthogonality and Bias Adjustment for Estimating Functions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 31(1), pages 93-114, March.
    • Handle: RePEc:bla:scjsta:v:31:y:2004:i:1:p:93-114
    DOI: 10.1111/j.1467-9469.2004.00375.x
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    1. Fabrizio Cipollini & Robert F. Engle & Giampiero M. Gallo, 2013. "Semiparametric Vector Mem," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 28(7), pages 1067-1086, November.
    2. Ip, Edward H. & Wang, Yuchung J., 2008. "A note on cuts for contingency tables," Journal of Multivariate Analysis, Elsevier, vol. 99(10), pages 2356-2363, November.
    3. Fabrizio Cipollini & Robert F. Engle & Giampiero M. Gallo, 2006. "Vector Multiplicative Error Models: Representation and Inference," NBER Technical Working Papers 0331, National Bureau of Economic Research, Inc.
    4. Rahma Abid & Célestin C. Kokonendji & Afif Masmoudi, 2021. "On Poisson-exponential-Tweedie models for ultra-overdispersed count data," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 105(1), pages 1-23, March.
    5. Maria Victoria Ibañez & Marina Martínez-Garcia & Amelia Simó, 2021. "A Review of Spatiotemporal Models for Count Data in R Packages. A Case Study of COVID-19 Data," Mathematics, MDPI, vol. 9(13), pages 1-23, July.
    6. Lambert, Philippe, 2021. "Fast Bayesian inference using Laplace approximations in nonparametric double additive location-scale models with right- and interval-censored data," Computational Statistics & Data Analysis, Elsevier, vol. 161(C).
    7. Stefano Cabras & María Castellanos & Erlis Ruli, 2014. "A Quasi likelihood approximation of posterior distributions for likelihood-intractable complex models," METRON, Springer;Sapienza Università di Roma, vol. 72(2), pages 153-167, August.
    8. Ricardo Rasmussen Petterle & Wagner Hugo Bonat & Cassius Tadeu Scarpin, 2019. "Quasi-beta Longitudinal Regression Model Applied to Water Quality Index Data," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 24(2), pages 346-368, June.
    9. Jørgensen, Bent & Demétrio, Clarice G.B. & Kristensen, Erik & Banta, Gary T. & Petersen, Hans Christian & Delefosse, Matthieu, 2011. "Bias-corrected Pearson estimating functions for Taylor's power law applied to benthic macrofauna data," Statistics & Probability Letters, Elsevier, vol. 81(7), pages 749-758, July.
    10. Rahma Abid & Célestin C. Kokonendji & Afif Masmoudi, 2020. "Geometric Tweedie regression models for continuous and semicontinuous data with variation phenomenon," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 104(1), pages 33-58, March.
    11. Osorio, Felipe & Gárate, Ángelo & Russo, Cibele M., 2024. "The gradient test statistic for outlier detection in generalized estimating equations," Statistics & Probability Letters, Elsevier, vol. 209(C).

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