Cantoni, Eva A robust approach to longitudinal data analysis. (English) Zbl 1056.62025 Can. J. Stat. 32, No. 2, 169-180 (2004). Summary: The author introduces robust techniques for estimation, inference and variable selection in the analysis of longitudinal data. She first addresses the problem of robust estimation of the regression and nuisance parameters, for which she derives the asymptotic distribution. She uses weighted estimating equations to build robust quasi-likelihood functions. These functions are then used to construct a class of test statistics for variable selection. She derives the limiting distribution of these tests and shows its robustness properties in terms of stability of the asymptotic level and power under contamination. An application to a real data set allows her to illustrate the benefits of a robust analysis. Cited in 17 Documents MSC: 62F10 Point estimation 62F35 Robustness and adaptive procedures (parametric inference) 62E20 Asymptotic distribution theory in statistics 62P10 Applications of statistics to biology and medical sciences; meta analysis 62F03 Parametric hypothesis testing Keywords:estimating equations; nuisance parameter estimation; quasi-likelihoods functions; robust estimation; robust variable selection; GUIDE study Software:ROBETH PDFBibTeX XMLCite \textit{E. Cantoni}, Can. J. Stat. 32, No. 2, 169--180 (2004; Zbl 1056.62025) Full Text: DOI Link References: [1] Cantoni, Robust inference for generalized linear models, Journal of the American Statistical Association 96 pp 1022– (2001) · Zbl 1072.62610 [2] Clarke, Nonsmooth analysis and Fréechet differentiability of M-functionals, Probability Theory and Related Fields 73 pp 197– (1986) [3] Devlin, Robust estimation of dispersion matrices and principal components, Journal of the American Statistical Association 76 pp 354– (1981) · Zbl 0463.62031 [4] Diggle, Analysis of Longitudinal Data. (1994) [5] Hampel, Robust Statistics: The Approach Based on Influence Functions. (1986) · Zbl 0593.62027 [6] Hanfelt, Approximate likelihood ratios for general estimating functions, Biometrika 82 pp 461– (1995) · Zbl 0831.62025 [7] Heritier, Robust bounded-influence tests in general parametric models, Journal of the American Statistical Association 89 pp 897– (1994) · Zbl 0804.62037 [8] Huber, Robust Statistics. (1981) [9] Huggins, A robust approach to the analysis of repeated measures, Biometrics 49 pp 715– (1993) [10] Johnson, Continuous Univariate Distributions 2 (1970) · Zbl 0213.21101 [11] Liang, Longitudinal data analysis using generalized linear models, Biometrika 73 pp 13– (1986) · Zbl 0595.62110 [12] Marazzi, Algorithms, Routines, and S Functions for Robust Statistics. (1993) · Zbl 0777.62004 [13] Maronna, Robust M-estimators of multivariate location and scatter, The Annals of Statistics 4 pp 51– (1976) · Zbl 0322.62054 [14] McCullagh, Quasi-likelihood functions, The Annals of Statistics 11 pp 59– (1983) · Zbl 0507.62025 [15] McCullagh, Generalized Linear Models (1989) · Zbl 0588.62104 [16] Mills, Marginally specified generalized linear mixed models: A robust approach, Biometrics 58 pp 727– (2002) · Zbl 1210.62098 [17] Preisser, Robust regression for clustered data with applications to binary regression, Biometrics 55 pp 574– (1999) · Zbl 1059.62570 [18] Prentice, Correlated binary regression with covariates specific to each binary observation, Biometrics 44 pp 1033– (1988) · Zbl 0715.62145 [19] Rao, Linear Statistical Inference and its Applications (1973) [20] Richardson, Robust restricted maximum likelihood in mixed linear models, Biometrics 51 pp 1429– (1995) · Zbl 0875.62313 [21] Wald, Test for statistical hypotheses concerning several parameters when the number of observations is large, Transactions of the American Mathematical Society 54 pp 426– (1943) · Zbl 0063.08120 [22] Wedderburn, Quasi-likelihood functions, generalized linear models, and the Gauss-Newton method, Biometrika 61 pp 439– (1974) · Zbl 0292.62050 [23] Zeger, Longitudinal data analysis for discrete and continuous outcomes, Bio-metries 42 pp 121– (1986) [24] Zeger, Models for longitudinal data: a generalized estimating equation approach, Biometrics 44 pp 1049– (1988) · Zbl 0715.62136 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.