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Modal regression based efficient and robust estimation for longitudinal partially linear models. (Chinese. English summary) Zbl 1474.62110

Summary: This paper considers the efficient and robust estimation for partially linear models with longitudinal data. By combining QR decomposition technique with quadratic inference functions technology, a modal regression based estimation procedure is proposed. We show that the resulting estimator of parametric component is consistent, and the asymptotic normality is obtained. In addition, we also show that the resulting estimator of nonparametric component is consistent with the optimal non-parametric convergence rate. Simulation study and real data analysis results indicate that the proposed method is more robust and effective.

MSC:

62G05 Nonparametric estimation
62G35 Nonparametric robustness
62G20 Asymptotic properties of nonparametric inference
62H11 Directional data; spatial statistics
62J05 Linear regression; mixed models