Adaptive Smoothing and Density-Based Tests of Multivariate Normality
研究了密度估计的自适应平滑方法，比较了其与固定核方法的性质，并基于此开发了两种多元正态性检验（积分平方误差和熵），进行了功效计算。
Abstract Methods of adaptive smoothing of density estimates, where the amount of smoothing applied varies according to local features of the underlying density, are investigated. The difficulties of applying Taylor series arguments in this context are explored. Simple properties of the estimates are investigated by numerical integration and compared with the fixed kernel approach. Optimal smoothing strategies, based on the multivariate Normal distribution, are derived. As an application of these techniques, two tests of multivariate Normality—one based on integrated squared error and one on entropy—are developed, and some power calculations are carried out. Key Words: AdaptiveDensity estimationMultivariate NormalitySmoothing