Goodness-of-fit test in high-dimensional linear sparse models

Sauvenier, Mathieu;Van Bellegem, Sébastien
(2023) , 14 pages

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A goodness-of-fit test for the outcome of variable selection in a high dimensional linear model is studied. The test minimizes a moment condition that reflects the sparsity constraint. Testing this constraint is possible thanks to a high dimensional central limit Theorem that is proved under heteroskedasticity. To implement the test a multiple-splitting projection test procedure that has been recently proposed in the literature is employed. Monte Carlo experiments demonstrate the power of the test. A real data application considers the problem of selecting predictors to nowcast quarterly GDP. The empirical results show that it is possible to select a minimal number of variables such that every larger set of variables would pass the goodness-of-fit test.
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Sauvenier, M., & Van Bellegem, S. (2023). Goodness-of-fit test in high-dimensional linear sparse models (LIDAM Discussion Paper CORE 2023/08). https://hdl.handle.net/2078.5/273326