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Dverview and Main Advances in Permutation Tests for Linear Regression Models

Journal of Mathematics and System Science 2015年第2期5卷 53-59页

作者： Massimiliano Giacalone Angela Alibrandi School of Economics Management and Statistics Bologna University Piazza Scaravilli 2 Bologna Italy. Department of Economical Business and Environmental Sciences and Quantitative Methods Messina University Via dei Verdi 75Messina ltaly.

When the population, from which the samples are extracted, is not normally distributed, or if the sample size is particularly reduced, become preferable the use of not parametric statistic test. An alternative to the normal model is the permutation or randomization model. The permutation model is nonparametric because no formal assumptions are made about the population parameters of the reference distribution, i.e., the distribution to which an obtained result is compared to determine its probability when the null hypothesis is true. Typically the reference distribution is a sampling distribution for parametric tests and a permutation distribution for many nonparametric tests. Within the regression models, it is possible to use the permutation tests, considering their ownerships of optimality, especially in the multivariate context and the normal distribution of the response variables is not guaranteed. In the literature there are numerous permutation tests applicable to the estimation of the regression models. The purpose of this study is to examine different kinds of permutation tests applied to linear models, focused our attention on the specific test statistic on which they are based. In this paper we focused our attention on permutation test of the independent variables, proposed by Oja, and other methods to effect the inference in non parametric way, in a regression model. Moreover, we show the recent advances in this context and try to compare them.

关键词： Permutation Tests Linear Regression Models non parametric approach.

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