Estimation of the number of components of nonparametric multivariate finite mixture models

We propose a novel estimator for the number of mixture components (denoted by M) in nonparametric finite model. The setting that we consider is one where analyst has repeated observations K?2 variables are conditionally independent given finitely supported latent variable with M support points. Under mild assumption on joint distribution observed and variables, show an integral operator T identified from data rank equal to M. use this observation, conjunction fact singular values operators stable under perturbations, M, which essentially consists thresholding rule counts consistent greater than data-driven threshold. prove our consistent, establish nonasymptotic results, provide sample performance guarantees estimator. present Monte Carlo study, shows performs well samples moderate size.