We employ a general Monte Carlo method to test composite hypotheses of goodness-of-fit for several popular multivariate models that can accommodate both asymmetry and heavy tails. Specifically, we consider weighted L2-type tests based on a discrepancy measure involving the distance between empirical characteristic functions and thus avoid the need for employing corresponding population quantities which may be unknown or complicated to work with. The only requirements of our tests are that we should be able to draw samples from the distribution under test and possess a reasonable method of estimation of the unknown distributional parameters. Monte Carlo studies are conducted to investigate the performance of the test criteria in finite samples for several families of skewed distributions. Real-data examples are also included to illustrate our method.

翻译：我们采用一种通用的蒙特卡洛方法来检验几种能够同时处理非对称性和重尾特性的流行多变量模型的复合拟合优度假设。具体而言，我们考虑基于经验特征函数距离的加权L2型检验统计量，从而避免使用可能未知或难以处理的对应总体量。该检验的唯一要求是能够从待检验分布中抽取样本，并具备未知分布参数的合理估计方法。通过蒙特卡洛研究，我们考察了该检验准则在有限样本下对几类偏态分布族的表现，并辅以实际数据案例说明该方法的应用。