Estimating Box-Cox power transformation parameter via goodness-of-fit tests
Estimating Box-Cox power transformation parameter via goodness-of-fit tests
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DOI：
10.1080/03610918.2014.957839
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发表时间：
2017-01-01
影响因子：
0.9
通讯作者：
Dag, Osman
中科院分区：
文献类型：
--
作者：
Asar, Ozgur;Ilk, Ozlem;Dag, Osman
Box-Cox幂变换是将数据的分布变换为正态分布的常用方法。该方法依赖于单个转换参数。在本研究中，我们将重点放在此参数的估计上。为此，我们使用了七个流行的正态分布的拟合优度检验，即Shapiro-Wilk检验、Anderson-Darling检验、Cramer-von Mise检验、Pearson卡方检验、Shapiro-Francia检验、Lilliefors检验和Jarque-Bera检验，并结合搜索算法。搜索算法的基础是根据测试找到最小或最大值的自变量，即，对于Shapiro-Wilk和Shapiro-Francia，最大值对于其余的是最小值。Dag等人的人工协变量方法。(2014)也包括在内，以供比较。为了比较这两种方法的性能，进行了仿真研究。结果表明，Shapiro-Wilk方法和人工协变量方法的效果较好，而Pearson卡方方法的效果最差。这些方法也被应用于两个真实的数据集。R包AID是为实现上述方法而提出的。
Box-Cox power transformation is a commonly used methodology to transform the distribution of the data into a normal distribution. The methodology relies on a single transformation parameter. In this study, we focus on the estimation of this parameter. For this purpose, we employ seven popular goodness-of-fit tests for normality, namely Shapiro-Wilk, Anderson-Darling, Cramer-von Mises, Pearson Chi-square, Shapiro-Francia, Lilliefors and Jarque-Bera tests, together with a searching algorithm. The searching algorithm is based on finding the argument of the minimum or maximum depending on the test, i.e., maximum for the Shapiro-Wilk and Shapiro-Francia, minimum for the rest. The artificial covariate method of Dag etal. (2014) is also included for comparison purposes. Simulation studies are implemented to compare the performances of the methods. Results show that Shapiro-Wilk and the artificial covariate method are more effective than the others and Pearson Chi-square is the worst performing method. The methods are also applied to two real-life datasets. The R package AID is proposed for implementation of the aforementioned methods.