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Register a new userA Goodness-of-Fit Test for Statistical Models
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Hangjin Jiang
Publication date
2020
fields
Mathematical Statistics
and research's language is
English
Authors
Hangjin Jiang
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Statistical modeling plays a fundamental role in understanding the underlying mechanism of massive data (statistical inference) and predicting the future (statistical prediction). Although all models are wrong, researchers try their best to make some of them be useful. The question here is how can we measure the usefulness of a statistical model for the data in hand? This is key to statistical prediction. The important statistical problem of testing whether the observations follow the proposed statistical model has only attracted relatively few attentions. In this paper, we proposed a new framework for this problem through building its connection with two-sample distribution comparison. The proposed method can be applied to evaluate a wide range of models. Examples are given to show the performance of the proposed method.
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We propose and analyse a novel nonparametric goodness of fit testing procedure for exchangeable exponential random graph models (ERGMs) when a single network realisation is observed. The test determines how likely it is that the observation is generated from a target unnormalised ERGM density. Our test statistics are derived from a kernel Stein discrepancy, a divergence constructed via Steins method using functions in a reproducing kernel Hilbert space, combined with a discrete Stein operator for ERGMs. The test is a Monte Carlo test based on simulated networks from the target ERGM. We show theoretical properties for the testing procedure for a class of ERGMs. Simulation studies and real network applications are presented.
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