Journal of the American Statistical Association · 1981 · 78 citations · 35 references
Natural SciencesMathematicsStatistical ComputingStatistical ModelingStatisticsDensity EstimationEstimation TheoryMonte Carlo MethodsMonte Carlo SimulationNonparametric StatisticsStatistical InferenceAccuracyData Analysis AlgorithmsData Processing AlgorithmsKernel SmoothingMonte Carlo ResamplingNonparametric Density EstimationProbability Density Function EstimationSmoothing Techniques
Abstract Although the theoretical properties of modern nonparametric probability density estimators have been studied for 25 years, there remains the practical problem of how to specify the amount of bias or smoothing in a density estimate based on a random sample. In this paper we review and evaluate three recently developed data-based algorithms that completely specify a density estimate from a random sample. Using Monte Carlo techniques, we compare the statistical accuracy of these algorithms as measured by the integrated mean squared error. In addition, we examine the sensitivity of these algorithms to outliers and estimate computer time requirements. One conclusion we draw is that the statistical accuracy of these data-based algorithms seems comparable to levels predicted by theoretical models.
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