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

Mathieu Sauvenier and Sébastien Van Bellegem
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Mathieu Sauvenier: Université catholique de Louvain, LIDAM/CORE, Belgium
Sébastien Van Bellegem: Université catholique de Louvain, LIDAM/CORE, Belgium

No 2023008, LIDAM Discussion Papers CORE from Université catholique de Louvain, Center for Operations Research and Econometrics (CORE)

Abstract: 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.

Keywords: High dimensional model; Sparsity; Goodness-of-Fit; Projection test; Nowcasting (search for similar items in EconPapers)
Pages: 14
Date: 2023-03-17
New Economics Papers: this item is included in nep-ecm and nep-ets
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