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

Author

Listed:
  • Sauvenier, Mathieu

    (Université catholique de Louvain, LIDAM/CORE, Belgium)

  • Van Bellegem, Sébastien

    (Université catholique de Louvain, LIDAM/CORE, Belgium)

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.

Suggested Citation

  • Sauvenier, Mathieu & Van Bellegem, Sébastien, 2023. "Goodness-of-fit test in high-dimensional linear sparse models," LIDAM Discussion Papers CORE 2023008, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvco:2023008
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    References listed on IDEAS

    as
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    Keywords

    High dimensional model ; Sparsity ; Goodness-of-Fit ; Projection test ; Nowcasting;
    All these keywords.

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