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On Wavelet Estimation of the Derivatives of a Density Based on Biased Data

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  • Yogendra P. Chaubey
  • Esmaeil Shirazi

Abstract

Here, we consider wavelet based estimation of the derivatives of a probability density function under random sampling from a weighted distribution and extend the results regarding the asymptotic convergence rates under the i.i.d. setup studied in Prakasa Rao (1996) to the biased-data setup. We compare the performance of the wavelet based estimator with that of the kernel based estimator obtained by differentiating the Efromovich (2004) kernel density estimator through a simulation study.

Suggested Citation

  • Yogendra P. Chaubey & Esmaeil Shirazi, 2015. "On Wavelet Estimation of the Derivatives of a Density Based on Biased Data," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 44(21), pages 4491-4506, November.
    • Handle: RePEc:taf:lstaxx:v:44:y:2015:i:21:p:4491-4506
    DOI: 10.1080/03610926.2013.851226
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    Cited by:

    1. Federico Palacios-González & Rosa M. García-Fernández, 2020. "A faster algorithm to estimate multiresolution densities," Computational Statistics, Springer, vol. 35(3), pages 1207-1230, September.

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