Smoothed inference and graphics via LP modeling
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Classical tests of goodness-of-fit aim to validate the conformity of a postulated model to the data under study. Given their inferential nature, they can be considered a crucial step in confirmatory data analysis. In their standard formulation, however, they do not allow exploring how the hypothesized model deviates from the truth nor do they provide any insight into how the rejected model could be improved to better fit the data. The main goal of this work is to establish a comprehensive framework for goodness-of-fit which naturally integrates modeling, estimation, inference and graphics. Modeling and estimation are conducted by generalizing smooth tests in the context of the novel LP approach to statistical modeling introduced by Mukhopadhyay and Parzen (2014). Inference and adequate post-selection adjustments are performed via an LP-based smoothed bootstrap and the results are summarized via an exhaustive graphical tool called CD-plot. Finally, the methods proposed are used to identify the distribution of the time from symptoms onset to hospitalization of COVID-19 patients.
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