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：多变量正常混合物模型下的强力估算总是一个计算挑战。 最近提出的一个最大假冒 \ b{eta} 类似估计值旨在按照最小密度功率差异(DPD)方法的精神估计MVN混合物模型的未知参数,但采用相对简单和可移动的计算算法,甚至对于较大的尺寸。在这封信中,我们将严格地推断最大伪伪伪值估计值的存在和薄弱一致性,如果是MVN混合物模型,则根据一套合理的假设。