Multivariate nonnegative orthant data are real vectors bounded to the left by the null vector, and they can be continuous, discrete or mixed. We first review the recent relative variability indexes for multivariate nonnegative continuous and count distributions. As a prelude, the classification of two comparable distributions having the same mean vector is done through under-, equi- and over-variability with respect to the reference distribution. Multivariate associated kernel estimators are then reviewed with new proposals that can accommodate any nonnegative orthant dataset. We focus on bandwidth matrix selections by adaptive and local Bayesian methods for semicontinuous and counting supports, respectively. We finally introduce a flexible semiparametric approach for estimating all these distributions on nonnegative supports. The corresponding estimator is directed by a given parametric part, and a nonparametric part which is a weight function to be estimated through multivariate associated kernels. A diagnostic model is also discussed to make an appropriate choice between the parametric, semiparametric and nonparametric approaches. The retention of pure nonparametric means the inconvenience of parametric part used in the modelization. Multivariate real data examples in semicontinuous setup as reliability are gradually considered to illustrate the proposed approach. Concluding remarks are made for extension to other multiple functions.
翻译:多变量非阴性或强度数据是真实的矢量,与空矢量左侧相连,可以是连续的、离散的或混合的。我们首先审查最近关于多变量非阴性连续和计数分布的相对变异指数。作为前奏,对具有相同平均值矢量分布的两种可比分布进行分类,通过参考分布的低度、等离性和超异性进行分类。然后审查多变量相关内核估量器,提出能够容纳任何非阴性或强性数据集的新建议。我们分别侧重于通过适应性和本地巴伊西亚方法选择带宽矩阵,以半相容和计数支持。我们最后采用了灵活的半分数方法来估算所有这些分布,作为前奏,对具有相同平均值的两种可比分布进行分类,通过给定的参数部分进行指导,而非参数部分则通过多变量相关内核值来估算。还讨论诊断模型,以便在参数、半偏差和非偏差性模型之间做出适当的选择。我们最后采用了一种灵活的半异性方法来估算所有这些分布式的可靠性。在拟议中,将精度的多变量用于解释性结论性结论性结论性结论性解释性结论性结论性结论性解释。在中,用于其他参数解释性结论性解释性解释性结论性结论性结论性解释性解释性解释性解释性结论性解释性解释性解释性结论性结论性结论性结论性结论性结论性解释。