Measurement Techniques

, Volume 62, Issue 9, pp 769–775 | Cite as

Nonparametric Estimation of the Quadratic Functional of a Multimodal Probability Density

  • A. V. LapkoEmail author
  • V. A. Lapko

A nonparametric method for estimating the mean square functional of a multimodal probability density of a one-dimensional random variable is examined. The proposed method is based on using the Sturgis and Heinhold–Gaede formulas and an optimum sampling procedure for sampling a range of values of random quantities. This method is compared with the traditional approach based on choosing a spread coefficient using the condition for the maximum of the likelihood function. The conditions for competence of this method are determined.


kernel estimate of probability density estimation of a functional of the probability density multimodal probability density choice of spread coefficient Sturges rule Heinhold–Gaede rule maximum likelihood criterion 


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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Institute of Computational ModelingSiberian Branch of the Russian Academy of SciencesKrasnoyarskRussia
  2. 2.Reshetnev Siberian State University of Science and TechnologyKrasnoyarskRussia

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