Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1152613 | Statistics & Probability Letters | 2011 | 7 Pages |
Abstract
Recent results show that densities of convolutions can be estimated by local U-statistics at the root-nn rate in various norms. Motivated by this and the fact that convolutions of normal densities are normal, we introduce new tests for normality which use as test statistics weighted L1L1-distances between the standard normal density and local U-statistics based on standardized observations. We show that such test statistics converge at the root-nn rate and determine their limit distributions as functionals of Gaussian processes. We also address a choice of bandwidth. Simulations show that our tests are competitive with other tests of normality.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Statistics and Probability
Authors
Anton Schick, Yishi Wang, Wolfgang Wefelmeyer,