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On a multivariate regression model for rates and proportions

机译：在利率和比例的多元回归模型上

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摘要

The paper by Johnson [Systems of frequency curves generated by the methods of translation, Biometrika 36 (2014), pp. 149-176] has introduced a very interesting univariate distribution with bounded support which is known in the statistical literature as the class of distributions. In this paper we generalize this class of univariate distributions to the multivariate case whose marginals are distributions. On the basis of the multivariate distribution introduced, we propose a multivariate regression model for dealing with multivariate response variables which are vectors of rates or proportions. We consider a frequentist approach to perform inferences, and the maximum likelihood method is employed to estimate the model parameters. Monte Carlo simulation results reveal that the maximum likelihood method can be used effectively in estimating the model parameters. An application to real data is presented to show the usefulness of the multivariate regression model in practice.
机译：Johnson的论文[通过翻译的方法生成的频率曲线的系统，Biometrika 36（2014），第149-176页]引入了一个非常有趣的带有有限支持的单变量分布，这在统计文献中被称为分布类别。在本文中，我们将这类一元分布推广为边际为分布的多元情况。基于引入的多元分布，我们提出了一个多元回归模型来处理多元响应变量，这些变量是比率或比例的向量。我们考虑一种常识性方法来执行推理，并采用最大似然法来估计模型参数。蒙特卡罗仿真结果表明，最大似然法可以有效地用于估计模型参数。提出了对实际数据的应用，以显示多元回归模型在实践中的有用性。

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