Smoothed Estimators for Markov Chains with Sparse Spatial Observations

Abstract

Empirical applications of the Markov chain model and its spatial extensions suffer from issues induced by the sparse transition probability matrix, which usually results from adopting maximum likelihood estimators (MLEs). Two discrete kernel estimators with cross-validated parameters are proposed for reducing the sparsity in the estimated transition probability matrix. Monte Carlo experiments suggest that these estimators are not only quite effective in producing a much less sparse matrix, alleviating issues related to sparsity, but also superior to MLEs in terms of lowering the mean squared error for individual and total transition probability, giving rise to the better recovery of the underlying dynamics.