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Nonparametric Estimate of a Parzen-Type Probability Density with an Implicitly Specified Form of the Kernel

  • GENERAL PROBLEMS OF METROLOGY AND MEASUREMENT TECHNIQUE
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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.

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References

  1. E. Parzen, “On estimation of a probability density function and mode,” Ann. Math. Stat., 33, No. 3, 1065–1076 (1962).

    Article  MathSciNet  MATH  Google Scholar 

  2. L. Devroye and L. Durphee, Nonparametric Estimation of Density (L 1 approach) [Russian translation], Mir, Moscow (1988).

    Google Scholar 

  3. V. A. Epanechnikov, “Nonparametric estimation of a multivariate probability density,” Teor. Veroyatn. Primen., 14, No. 1, 156–161 (1969).

    MATH  Google Scholar 

  4. A. V. Lapko and V. A. Lapko, “Analysis of the properties of a mixture of nonparametric estimates of the probability densities of a multivariate random variable,” Vest. SibGAU, No. 2, 32–35 (2010).

  5. A. V. Lapko and V. A. Lapko, “Regression estimate of the multidimensional probability density and its properties,” Opto-Electron., Instrum. Data Proc., 50, No. 2, 148–153 (2014).

    Article  Google Scholar 

  6. R. P. W. Duin, “On the choice of smoothing parameters for Parzen estimators of probability density functions,” IEE Trans. Comp., C-25, 1175–1179 (1976).

    Article  MathSciNet  MATH  Google Scholar 

  7. H. A. Sturges, “The choice of class interval,” J. Am. Stat. Assoc., 65–66 (1926).

  8. I. Heinhold and K. Gaede, Ingenieur Statistik, Springer, Munich, Vienna (1964).

    MATH  Google Scholar 

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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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Authors and Affiliations

  1. Institute of Computational Modelling, Siberian Branch of the Russian Academy of Sciences, Krasnoyarsk, Russia

    A. V. Lapko & V. A. Lapko

  2. Siberian State Aerospace University, Krasnoyarsk, Russia

    A. V. Lapko & V. A. Lapko

Authors
  1. A. V. Lapko
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  2. V. A. Lapko
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Correspondence to A. V. Lapko.

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Translated from Izmeritel’naya Tekhnika, No. 6, pp. 14–17, June, 2016.

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Lapko, A.V., Lapko, V.A. Nonparametric Estimate of a Parzen-Type Probability Density with an Implicitly Specified Form of the Kernel. Meas Tech 59, 571–576 (2016). https://doi.org/10.1007/s11018-016-1010-5

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  • DOI: https://doi.org/10.1007/s11018-016-1010-5

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