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Robust likelihood inference for multivariate correlated count data. (English) Zbl 1347.65035

Summary: A parametric robust approach for analyzing correlated count data is introduced. This method enables one to construct an asymptotically valid likelihood for the regression parameter when knowledge about the joint distribution for data is scarce or not available. We use simulations and real data analysis to demonstrate the merit of the proposed robust likelihood method.

MSC:

62-08 Computational methods for problems pertaining to statistics
62F35 Robustness and adaptive procedures (parametric inference)
62H12 Estimation in multivariate analysis
62F12 Asymptotic properties of parametric estimators

Software:

MASS (R); R; robustbase
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Full Text: DOI

References:

[1] Alfo M, Trovato G (2004) Semiparametric mixture models for multivariate count data, with application. Econom J 7:426-454 · Zbl 1064.62031
[2] Bartlett MS (1953) Approximate confidence intervals. Biometrika 40:12-19 · Zbl 0050.36302
[3] Berkhout P, Plug E (2004) A bivariate Poisson count data model using conditional probabilities. Stat Neerl 58:349-364 · Zbl 1059.62011
[4] Cameron AC, Li T, Trivedi K, Zimmer DM (2004) Modelling the differences in counted outcomes using bivariate copula models with application to mismeasured counts. Econom J 7:566-584 · Zbl 1115.62329
[5] Cox DR, Hinkley DV (1986) Theoretical statistics. Chapman and Hall, New York · Zbl 0334.62003
[6] Cox DR, Reid N (1987) Parameter orthogonality and approximate conditional inference. J R Stat Soc B 49:1-39 · Zbl 0616.62006
[7] Diggle PJ, Liang KY, Zeger SL (1994) Analysis of longitudinal data. Oxford University Press, Oxford · Zbl 1031.62002
[8] Fiocco M, Putter H, Van Houwelingen JC (2009) A new serially correlated gamma-frailty process for longitudinal count data. Biostatistics 10:245-257 · Zbl 1437.62458
[9] Gurmu S, Elder J (2007) A simple bivariate count data regression model. Econ Bull 3:1-10 · Zbl 0945.91053
[10] Hadgu A, Koch G (1999) Application of generalized estimating equations to a dental randomized clinical trial. J Biopharm Stat 9:161-178 · Zbl 0930.62101
[11] Hauck WW, Donner A (1977) Wald’s test as applied to hypotheses in logit analysis. J Am Stat Assoc 72:851-853 · Zbl 0375.62022
[12] Huber PJ (1981) Robust statistics. Wiley, New York · Zbl 0536.62025
[13] Kauermann G, Carroll RJ (2001) A note on the efficiency of sandwich covariance matrix estimation. J Am Stat Assoc 96:1387-1396 · Zbl 1073.62539
[14] Liang KY, Zeger SL (1986) Longitudinal data analysis using generalized linear models. Biometrika 73:13-22 · Zbl 0595.62110
[15] Maronna R, Martin D, Yohai V (2006) Robust statistics: theory and methods. Wiley, West Sussex · Zbl 1094.62040
[16] McCullagh P (1983) Quasi-likelihood functions. Ann Stat 11:59-67 · Zbl 0507.62025
[17] R Core Team (2014) R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. http://www.R-project.org/
[18] Royall RM (2000) On the probability of observing misleading statistical evidence (with discussion). J Am Stat Assoc 95:760-780 · Zbl 1013.62002
[19] Royall RM, Tsou TS (2003) Interpreting statistical evidence using imperfect models: robust adjusted likelihood functions. J R Stat Soc Ser B 65:391-404 · Zbl 1065.62047
[20] Solis-Trapala IL, Farewell VT (2005) Regression analysis of overdispersed correlated count data with subject specific covariates. Stat Med 24:2557-2575
[21] Stafford JE (1996) A robust adjustment of the profile likelihood. Ann Stat 24:336-352 · Zbl 0905.62027
[22] Thall PF, Vail SC (1990) Some covariance models for longitudinal count data with overdispersion. Biometrics 46:57-671 · Zbl 0712.62048
[23] Turesky S, Gilmore ND, Glickman J (1970) Reduced plaque formation by the chloromethyl analogue of Victamine. J Periodontol 41:41
[24] Venables WN, Ripley BD (2002) Modern applied statistics with S, 4th edn. Springer, New York · Zbl 1006.62003
[25] White H (1982) Maximum likelihood estimation of misspecified models. Econometrica 50:1-25 · Zbl 0478.62088
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