Nonparametric Estimate of a Parzen-Type Probability Density with an Implicitly Specified Form of the Kernel
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A nonparametric estimate for the probability density is proposed with better approximation properties than the traditional Rosenblatt–Parzen statistics. The dependences of its properties on the form of the kernel function and on the formulas for the sampling interval for the random quantity are discussed.
Keywordsprobability density nonparametric Rosenblatt–Parzen estimate approximation properties kernel function Sturges’ rule Heinhold–Gaede formula
This work was carried out within the framework of the project part of State Assignment of Ministry of Education and Science of Russia (No. 2.914.2014/K).
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