The proposed multiple scaled contaminated asymmetric Laplace (MSCAL) distribution is an extension of the multivariate asymmetric Laplace distribution to allow for a different excess kurtosis on each dimension and for more flexible shapes of the hyper-contours. These peculiarities are obtained by working on the principal component (PC) space. The structure of the MSCAL distribution has the further advantage of allowing for automatic PC-wise outlier detection – i.e., detection of outliers separately on each PC – when convenient constraints on the parameters are imposed. The MSCAL is fitted using a Monte Carlo expectation-maximization (MCEM) algorithm that uses a Monte Carlo method to estimate the orthogonal matrix of eigenvectors. A simulation study is used to assess the proposed MCEM in terms of computational efficiency and parameter recovery. In a real data application, the MSCAL is fitted to a real data set containing the anthropometric measurements of monozygotic/dizygotic twins. Both a skewed bivariate subset of the full data, perturbed by some outlying points, and the full data are considered.

所提出的多尺度污染非对称拉普拉斯 (MSCAL) 分布是多元非对称拉普拉斯分布的扩展，允许每个维度上有不同的超额峰度以及更灵活的超轮廓形状。这些特性是通过主成分 (PC) 空间获得的。 MSCAL 分布的结构还有一个优点，即当对参数施加方便的约束时，允许自动进行 PC 级异常值检测，即在每台 PC 上单独检测异常值。 MSCAL 使用蒙特卡罗期望最大化 (MCEM) 算法进行拟合，该算法使用蒙特卡罗方法来估计特征向量的正交矩阵。仿真研究用于评估所提出的 MCEM 的计算效率和参数恢复。在实际数据应用中，MSCAL 适合包含同卵双胞胎/异卵双胞胎的人体测量数据的真实数据集。受一些外围点扰动的完整数据的倾斜二变量子集和完整数据都被考虑。