Directed likelihood statistic in symmetric regressions

Artur J. Lemonte ()
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Artur J. Lemonte: Universidade Federal do Rio Grande do Norte

Statistical Papers, 2025, vol. 66, issue 7, No 4, 20 pages

Abstract: Abstract The class of symmetric regression models corresponds to a wide class of models and it can be quite useful for modeling many types of real data that occur frequently in practice. It encompasses important models like the normal, Student-t, and power exponential regression models, among others. In this paper, we focus on hypothesis testing inference on the parameters of this class of models for small-sized samples. To do so, we consider the directed likelihood test statistic. Monte Carlo simulation experiments reveal that this test statistic does not perform well, mainly in small samples. To overcome this shortcoming, we derive an adjustment factor to the directed likelihood test statistic based on an orthogonal parametrization introduced in this paper. We verify that the modified directed likelihood test statistic leads to very accurate inference even for very small samples. Real data applications are also considered for illustrative purposes.

Keywords: Large sample test; Maximum likelihood estimation; Parametric inference; Signed likelihood ratio test; Symmetric distribution; 62F03; 62J05 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s00362-025-01772-0

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