Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5129532 | Journal of Statistical Planning and Inference | 2017 | 25 Pages |
â¢We study in detail the bias and variance of the entropy estimator proposed by Kozachenko and Leonenko (1987) for a large class of densities on Rd.â¢We then use the work of Bickel and Breiman (1983) to prove a central limit theorem in dimensions 1 and 2.â¢In higher dimensions, we provide a development of the bias in terms of powers of Nâ2/d.â¢This allows us to use a Richardson extrapolation to build, in any dimension, a root-n consistent entropy estimator satisfying a central limit theorem which allows for explicit (asymptotic) confidence intervals.â¢To our knowledge, all the previous general root-n consistency results were concerning dimension 1.
We study in detail the bias and variance of the entropy estimator proposed by Kozachenko and Leonenko (1987) for a large class of densities on Rd. We then use the work of Bickel and Breiman (1983) to prove a central limit theorem in dimensions 1 and 2. In higher dimensions, we provide a development of the bias in terms of powers of Nâ2/d. This allows us to use a Richardson extrapolation to build, in any dimension, a root-n consistent entropy estimator satisfying a central limit theorem which allows for explicit (asymptotic) confidence intervals. To our knowledge, all the previous general root-n consistency results were concerning dimension 1.