[ABE-L] Seminário - IME-USP - Modelos de Regressão e Aplicações - Small-sample testing inference in symmetric and log-symmetric linear regression models

[Silvia Ferrari]

Seminário - Projeto Temático: Modelos de Regressão e Aplicações

Título: Small-sample testing inference in symmetric and log-symmetric
linear regression models

Palestrante: Francisco Moisés Medeiros – Pós-Graduação, Estatística, IME-USP

Quando: 18 de março, sexta-feira, às 11h.

Onde: Auditório Jacy Monteiro, Bloco B, piso térreo - IME-USP

Resumo. This paper deals with the issue of testing hypothesis in symmetric
and log-symmetric linear regression models in small and moderate-sized
samples. We focus on four tests, namely the Wald, likelihood ratio, score,
and gradient tests. These tests rely on asymptotic results and are
unreliable when the sample size is not large enough to guarantee a good
agreement between the exact distribution of the test statistic and the
corresponding chi-squared asymptotic distribution. Bartlett and
Bartlett-type corrections typically attenuate the size distortion of the
tests. These corrections are available in the literature for the likelihood
ratio and score tests in symmetric linear regression models. Here, we
derive a Bartlett-type correction for the gradient test. We show that the
corrections are also valid for the log-symmetric linear regression models.
We numerically compare the various tests, and bootstrapped tests, through
simulations. Our results suggest that the corrected and bootstrapped tests
exhibit type I probability error closer to the chosen nominal level with
virtually no power loss. The analytically corrected tests, including the
Bartlett-corrected gradient test derived in this paper, perform as well as
the bootstrapped tests with the advantage of not requiring
computationally-intensive calculations. We present two real data
applications to illustrate the usefulness of the modified tests.

Joint work with Silvia L. P. Ferrari.
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