Robust estimation in generalized semiparametric mixed models for longitudinal data. (English) Zbl 1122.62029
Summary: We consider robust generalized estimating equations for the analysis of semiparametric generalized partial linear mixed models (GPLMMs) for longitudinal data. We approximate the nonparametric function in the GPLMM by a regression spline, and make use of bounded scores and leverage-based weights in the estimating equation to achieve robustness against outliers and influential data points, respectively. Under some regularity conditions, the asymptotic properties of the robust estimators are investigated. To avoid the computational problems involving high-dimensional integrals in our estimators, we adopt a robust Monte Carlo Newton-Raphson (RMCNR) algorithm for fitting GPLMMs. Small simulations are carried out to study the behavior of the robust estimates in the presence of outliers, and these estimates are also compared to their corresponding non-robust estimates. The proposed robust method is illustrated in the analysis of two real data sets.
MSC:
| 62G08 | Nonparametric regression and quantile regression |
| 62G35 | Nonparametric robustness |
| 62J12 | Generalized linear models (logistic models) |
| 62F35 | Robustness and adaptive procedures (parametric inference) |
| 65C05 | Monte Carlo methods |
| 62G20 | Asymptotic properties of nonparametric inference |
Keywords:
\(B\)-spline; longitudinal data; Metropolis algorithm; mixed model; Newton-Raphson algorithm; partial linear models; robustnessReferences:
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