Tests for normality based on density estimators of convolutions

Anton Schick, Yishi Wang and Wolfgang Wefelmeyer

Statistics & Probability Letters, 2011, vol. 81, issue 2, 337-343

Abstract: Recent results show that densities of convolutions can be estimated by local U-statistics at the root-n 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 L1-distances between the standard normal density and local U-statistics based on standardized observations. We show that such test statistics converge at the root-n 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: Convolution-type; kernel; density; estimator; Goodness-of-fit; test (search for similar items in EconPapers)
Date: 2011
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Citations: View citations in EconPapers (4)

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