Vector quantization and clustering in the presence of censoring

We consider the problem of optimal vector quantization for random vectors with one censored component and applications to clustering of censored observations. We introduce the definitions of the empirical distortion and of the empirically optimal quantizer in the presence of censoring and we establish the almost sure consistency of empirical design. Moreover, we provide a non asymptotic exponential bound for the difference between the performance of the empirically optimal k-quantizer and the optimal performance over the class of all k-quantizers. As a natural application of the new quantization criterion, we propose an iterative two-step algorithm allowing for clustering of multivariate observations with one censored component. This method is investigated numerically through applications to real and simulated data.