@article{oai:ynu.repo.nii.ac.jp:00006834, author = {Fotopoulos, S. B.}, issue = {2}, journal = {Yokohama Mathematical Journal = 横濱市立大學紀要. D部門, 数学}, month = {}, note = {application/pdf, The density estimator $f_{¥tau_{n}}(t)=T_{¥overline{n}^{1}}¥sum_{j=1}^{¥tau_{n}}h_{j}^{-1}K((t-X_{j})/h_{j})$ is considered, where $T_{n}$ is a random index. A sharp rate of convergence for the uniform distance between the probability of $f_{¥tau_{n}}(t)$ , when Properly normed, and the standard normal distribution is obtained. It is shown that for any $¥epsilon>0$ , the cptimum order of the uniform estimate is $0(n^{-1/3+¥epsilon})$ . Similar results have been shown by other authors, but under different assumptions on $T_{n}$ .}, pages = {89--105}, title = {ON THE RATE OF CONVERGENCE FOR SEQUENTIAL DENSITY ESTIMATION}, volume = {39}, year = {1992} }