On Some Convergence Results with Random Bandwidths in Density Estimation
Prof. Alok, GoswamiISI, Kolkata, India 下午 2:30–4:00 鴻經館 107 室摘要：
Kernel-based estimators have been widely used for estimating unknown density for a very long time. Consistency properties of such estimators depend on proving convergence results. Different forms of convergence results have been proved by various authors under various conditions. Weid and Weissbach (2010) give a very good account of the known convergence results. However, most of these results are for kernel density estimators with non-random bandwidths. However, the practical applications of kernel-density estimation depend very crucially on efficient algorithms for data-based choice of the bandwidth., thus making random bandwidth selection a very important part of kernel density estimation. However, proving convergence results for such estimators with random bandwidth have proved to be generally harder. In this talk, some new convergence results for the random bandwidth case will be discussed.