Monte Carlo Strategies in Scientific Computing
Monte Carlo Strategies in Scientific Computing
Exact computation of bivariate projection depth and the Stahel-Donoho estimator
Computational Statistics & Data Analysis
Monte Carlo Statistical Methods
Monte Carlo Statistical Methods
Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images
IEEE Transactions on Pattern Analysis and Machine Intelligence
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Data depth for multivariate data has received considerable attention in multivariate nonparametric analysis and robust statistics. Nevertheless, the computation of data depth such as projection depth has remained as a very challenging problem which hinders the development of the projection depth and its wide use in practice. Especially in high dimension, there is no efficient algorithm for the computation of the projection depth and its induced estimators (including the Stahel-Donoho estimator as a special case). In this paper, we employ simulated annealing algorithm by invoking Markov Chain Monte Carlo technique to compute the projection depth. Simulation results show that this new approximate method performs significantly better than its competitors. In lower dimension, we are able to show that the approximate results from this algorithm are very close to the exact ones.