Title: Imputation of missing values by pseudo-marginal simulated annealing algorithm using depth statistics
Authors: Randal Douc - Telecom SudParis (France)
Pavlo Mozharovskyi - Telecom Paris, Institut Polytechnique de Paris (France)
Francois Roueff - Telecom Paris (France)
Kimsy Tor - Telecom ParisTech (France) [presenting]
Abstract: The problem of missing data is peculiar to many applications and often impedes statistical analysis. One of the universal ways to deal with missing values is their imputation prior to employment of the statistical method in question. Since model-based imputation approaches are limited to particular data-generating processes, non-parametric imputation methods have been proposed in the literature. These however induce high computational cost due to parameter tuning and suffer from the curse of dimensionality. We propose a new imputation method based on the non-parametric robust measure of centrality called data depth. The depth statistics is used to generate a family of models which are then fitted simultaneously using the pseudo-marginal simulated annealing algorithm. The created models are chosen to be simple enough to be easily fitted and flexible enough to suit many applications. Multiple imputed data sets constitute direct output of the procedure while single imputation can be obtained by their averaging, which makes the method suitable for both estimation and inference. Simulation and real-data studies illustrate competitive performance of the proposed approach.