Jankowski, HannaBoonpatcharanon, Sawitree2019-11-222019-11-222019-052019-11-22http://hdl.handle.net/10315/36721Maximum likelihood estimation of a log-concave density has certain advantages over other nonparametric approaches, such as kernel density estimation, which requires a bandwidth selection. Furthermore, finding the optimal bandwidth gets more difficult as a dimension increases. On the other hand, the shape-constrained approach is automatic and does not need any tuning parameters. However, for both the kernel and log-concave estimators, the rate of convergence slows down as the dimension d increases. To handle this "curse of dimensionality", we study an intermediate semi-parametric copula approach and we estimate the marginals using the log-concave shape-constrained MLE and use a parametric approach to fit the copula parameters. We prove square root n rate of convergence for the parametric estimator and that the joint density converges at a rate of n^(-2/5) regardless of dimension. This is faster than the conjectured rate of n^(-2/(d+4)) for the multivariate log-concave estimators. We examine the performance of our proposed method via simulation studies and real data example.Author owns copyright, except where explicitly noted. Please contact the author directly with licensing requests.StatisticsElectronic Thesis or Dissertation2019-11-22semi-parametriclog-concavecopuladensity estimation