Composite Goodness-of-fit Tests with Kernels

Model misspecification can create significant challenges for the implementation of probabilistic models, and this has led to development of a range of inference methods which directly account for the issue. However, these method tend to lose efficiency and should only be used when the model is really misspecified. Unfortunately, there is a lack of generally applicable methods to test whether this is the case or not. One set of tools which can help are goodness-of-fit tests, which can test whether a dataset has been generated from a fixed distribution. Kernel-based tests have been developed to for this problem, and these are popular due to their flexibility, strong theoretical guarantees and ease of implementation in a wide range of scenarios. In this paper, we extend this line of work to the more challenging composite goodness-of-fit problem, where we are instead interested in whether the data comes from any distribution in some parametric family.

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