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This article proposes robust estimation via modified Cholesky decomposition for modal partially nonlinear models with longitudinal data. A new minorization-maximization algorithm is developed to calculate the modal regression estimates, and the balance between the robustness and efficiency can be achieved by choosing appropriate data adaptive bandwidth. Simulation studies and real data analysis are conducted to illustrate the finite sample performance of the proposed approach.

Robust estimation via modified Cholesky decomposition for modal partially nonlinear models with longitudinal data