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Abstract:
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Time-varying coefficient models are widely used in longitudinal data analysis. Those models allow the effects of predictors on response to vary over time. In this presentation, we consider a mixed-effects time-varying coefficient model to account for the within subject correlation for longitudinal data. We show that when the kernel smoothing method is used to estimate the smooth functions in time-varying coefficient models for sparse or dense longitudinal data, the asymptotic results of these two situations are essentially different. Therefore, a subjective choice between the sparse and dense cases might lead to erroneous conclusions for statistical inference. In order to solve this problem, we establish a unified self-normalized central limit theorem, based on which a unified inference is proposed without deciding whether the data are sparse or dense. The effectiveness of the proposed unified inference is demonstrated through a simulation study and an analysis of an acquired immune deficiency syndrome (AIDS) data set.
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