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hermiter: R package for sequential nonparametric estimation

Author

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  • Michael Stephanou

    (Rand Merchant Bank)

  • Melvin Varughese

    (University of Cape Town
    University of Western Australia)

Abstract

This article introduces the R package hermiter which facilitates estimation of univariate and bivariate probability density functions and cumulative distribution functions along with full quantile functions (univariate) and nonparametric correlation coefficients (bivariate) using Hermite series based estimators. The algorithms implemented in the hermiter package are particularly useful in the sequential setting (both stationary and non-stationary) and one-pass batch estimation setting for large data sets. In addition, the Hermite series based estimators are approximately mergeable allowing parallel and distributed estimation.

Suggested Citation

  • Michael Stephanou & Melvin Varughese, 2024. "hermiter: R package for sequential nonparametric estimation," Computational Statistics, Springer, vol. 39(3), pages 1127-1163, May.
    • Handle: RePEc:spr:compst:v:39:y:2024:i:3:d:10.1007_s00180-023-01382-0
    DOI: 10.1007/s00180-023-01382-0
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    References listed on IDEAS

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    1. Michael Stephanou & Melvin Varughese, 2021. "On the properties of hermite series based distribution function estimators," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(4), pages 535-559, May.
    2. Christophe Croux & Catherine Dehon, 2010. "Influence functions of the Spearman and Kendall correlation measures," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 19(4), pages 497-515, November.
    3. Mildenberger, Thoralf & Weinert, Henrike, 2012. "The benchden Package: Benchmark Densities for Nonparametric Density Estimation," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 46(i14).
    4. Greblicki, Wlodzimierz & Pawlak, Miroslaw, 1985. "Pointwise consistency of the hermite series density estimate," Statistics & Probability Letters, Elsevier, vol. 3(2), pages 65-69, April.
    5. Greblicki, W?odzimierz & Pawlak, Miros?aw, 1984. "Hermite series estimates of a probability density and its derivatives," Journal of Multivariate Analysis, Elsevier, vol. 15(2), pages 174-182, October.
    6. E. Liebscher, 1990. "Hermite series estimators for probability densities," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 37(1), pages 321-343, December.
    7. Asma Jmaei & Yousri Slaoui & Wassima Dellagi, 2017. "Recursive distribution estimator defined by stochastic approximation method using Bernstein polynomials," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 29(4), pages 792-805, October.
    8. Stephanou, Michael & Varughese, Melvin, 2021. "Sequential estimation of Spearman rank correlation using Hermite series estimators," Journal of Multivariate Analysis, Elsevier, vol. 186(C).
    9. Eddelbuettel, Dirk & Francois, Romain, 2011. "Rcpp: Seamless R and C++ Integration," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 40(i08).
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