  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.
