On variable selection in joint modeling of mean and dispersion

IF 0.6 4区 数学 Q4 STATISTICS & PROBABILITY Brazilian Journal of Probability and Statistics Pub Date : 2021-09-16 DOI:10.1214/21-bjps512
E. R. Pinto, Leandro Pereira
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引用次数: 2

Abstract

The joint modeling of mean and dispersion (JMMD) provides an efficient method to obtain useful models for the mean and dispersion, especially in problems of robust design experiments. However, in the literature on JMMD there are few works dedicated to variable selection and this theme is still a challenge. In this article, we propose a procedure for selecting variables in JMMD, based on hypothesis testing and the quality of the model's fit. A criterion for checking the goodness of fit is used, in each iteration of the selection process, as a filter for choosing the terms that will be evaluated by a hypothesis test. Three types of criteria were considered for checking the quality of the model fit in our variable selection procedure. The criteria used were: the extended Akaike information criterion, the corrected Akaike information criterion and a specific criterion for the JMMD, proposed by us, a type of extended adjusted coefficient of determination. Simulation studies were carried out to verify the efficiency of our variable selection procedure. In all situations considered, the proposed procedure proved to be effective and quite satisfactory. The variable selection process was applied to a real example from an industrial experiment.
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均值与离散度联合建模中的变量选择
均值与色散的联合建模(JMMD)提供了一种有效的方法来获得有用的均值与色散模型,特别是在鲁棒设计实验问题中。然而,在JMMD的文献中,很少有专门研究变量选择的作品,这一主题仍然是一个挑战。在本文中,我们提出了一种基于假设检验和模型拟合质量的JMMD中选择变量的程序。在选择过程的每次迭代中,检查拟合优度的标准被用作选择将由假设检验评估的项的过滤器。在我们的变量选择过程中,考虑了三种类型的标准来检查模型拟合的质量。使用的标准是:扩展的赤池信息准则,修正的赤池信息准则和我们提出的JMMD的特定准则,一种扩展的调整的决定系数。模拟研究进行了验证我们的变量选择程序的效率。在所有考虑到的情况下,所提议的程序证明是有效的和相当令人满意的。将变量选择过程应用于工业实验的实际实例。
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来源期刊
CiteScore
1.60
自引率
10.00%
发文量
30
审稿时长
>12 weeks
期刊介绍: The Brazilian Journal of Probability and Statistics aims to publish high quality research papers in applied probability, applied statistics, computational statistics, mathematical statistics, probability theory and stochastic processes. More specifically, the following types of contributions will be considered: (i) Original articles dealing with methodological developments, comparison of competing techniques or their computational aspects. (ii) Original articles developing theoretical results. (iii) Articles that contain novel applications of existing methodologies to practical problems. For these papers the focus is in the importance and originality of the applied problem, as well as, applications of the best available methodologies to solve it. (iv) Survey articles containing a thorough coverage of topics of broad interest to probability and statistics. The journal will occasionally publish book reviews, invited papers and essays on the teaching of statistics.
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