Hoyos AEP, Fossaluza V, Esteves LG, de Bragança Pereira CA. Adaptive Significance Levels in Tests for Linear Regression Models: The
e-Value and
P-Value Cases.
Entropy (Basel) 2022;
25:e25010019. [PMID:
36673160 PMCID:
PMC9858150 DOI:
10.3390/e25010019]
[Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/27/2022] [Revised: 11/17/2022] [Accepted: 12/16/2022] [Indexed: 05/28/2023]
Abstract
The full Bayesian significance test (FBST) for precise hypotheses is a Bayesian alternative to the traditional significance tests based on p-values. The FBST is characterized by the e-value as an evidence index in favor of the null hypothesis (H). An important practical issue for the implementation of the FBST is to establish how small the evidence against H must be in order to decide for its rejection. In this work, we present a method to find a cutoff value for the e-value in the FBST by minimizing the linear combination of the averaged type-I and type-II error probabilities for a given sample size and also for a given dimensionality of the parameter space. Furthermore, we compare our methodology with the results obtained from the test with adaptive significance level, which presents the capital-P P-value as a decision-making evidence measure. For this purpose, the scenario of linear regression models with unknown variance under the Bayesian approach is considered.
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