Robust estimation under multivariate normal (MVN) mixture model is always a computational challenge. A recently proposed maximum pseudo \b{eta}-likelihood estimator aims to estimate the unknown parameters of a MVN mixture model in the spirit of minimum density power divergence (DPD) methodology but with a relatively simpler and tractable computational algorithm even for larger dimensions. In this letter, we will rigorously derive the existence and weak consistency of the maximum pseudo \b{eta}-likelihood estimator in case of MVN mixture models under a reasonable set of assumptions.

翻译：在多元正态（MVN）混合模型下进行稳健估计始终是一项计算挑战。最近提出的一种最大伪β-似然估计量，旨在以最小密度幂散度（DPD）方法为精神，估计MVN混合模型中的未知参数，同时即使在较高维数下也能采用相对简单且易于处理的计算算法。在本文中，我们将在一组合理假设条件下，严格推导MVN混合模型中最大伪β-似然估计量的存在性与弱一致性。