Thời gian: 14h Thứ 5, ngày 2/11/2023

Địa điểm: Phòng 507 nhà A6

Tóm tắt: In this work, more than 40 different estimators of the Shannon differential entropy based on different estimation techniques are reviewed. The estimation techniques considered include the sample spacings, kernel density estimation and the k−nearest neighbour. The performance of the estimators based on the three techniques is known to depend on the window size (m), bandwidth (h), and the number of nearest neighbours (k), respectively. Optimal values of these parameters are considered in each technique for different sample sizes and variable dimensions. The estimators are compared empirically through extensive simulation studies. The empirical comparisons are carried out at different sample sizes and different variable dimensions for different groups of continuous distributions. The asymptotic behaviour of the estimators are also compared theoretically for different d−dimensional spaces. Based on the results, different procedures for testing d−dimensional normality are proposed.

Keywords: asymptotic behaviour, extensive simulation, k−nearest neighbour, kernel density estimation, window size spacing, bias and mean square error of an estimator.

Mathematics Subject Classi cation: 62E10; 62G05; 62G20; 62H12.