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Being a sonnet cycle of love with a detailed description of the lady’s physical beauty and the lover’s happy feelings, Amorettiis a story of love between earthlings which is aimed at marriage. Meanwhile, Spenser sanctifies the love by Platonizing and Christianizing the lady. Thus it is clear that the love in the mind of Spenser is not just an earthly one or a heavenly one separately, but both, and, a combination of both earthly love and sacred love.
Time-varying coefficient models are useful in longitudinal data analysis. Various efforts have been invested for the estimation of the coefficient functions, based on the least squares principle. Related work includes smoothing spline and kernel methods among others, but these methods suffer from the shortcoming of non-robustness. In this paper, we introduce a local M-estimation method for estimating the coefficient functions and develop a robustified generalized likelihood ratio (GLR) statistic to test if some of the coefficient functions are constants or of certain parametric forms. The robustified GLR test is robust against outliers and the error distribution. This provides a useful robust inference tool for the models with longitudinal data. The bandwidth selection issue is also addressed to facilitate the implementation in practice. Simulations show that the proposed testing method is more powerful in some situations than its counterpart based on the least squares principle. A real example is also given for illustration.