Journal of the American Statistical Association · 1993 · 33 citations · 0 references
ComputingBiostatisticsEconometricsStatistical LearningTime Series AnalysisDensity AnalysisDensity EstimationKernel Density EstimationKernel MethodsMultivariate AnalysisAdaptive Kernel Density EstimationAdaptive SmoothingDensity SmoothingKernel SmoothingMultivariate Density EstimationMultivariate Normal DistributionSmoothingSmoothing Techniques
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