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Improvements on strong uniform consistency of some known kernel estimates of a density and its derivatives

Author

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  • Karunamuni, R. J.
  • Mehra, K. L.

Abstract

Some known kernel type estimates of a density and its derivatives f(p) are considered. Strong uniform consistency properties over the whole real line are studied. Improved rate of convergence results are established under substantially weaker smoothness assumptions of f(p), p [greater-or-equal, slanted] 0. A new bias reduction technique is presented based on Bernstein's polynomials and notions and relations in calculous of finite differences.

Suggested Citation

  • Karunamuni, R. J. & Mehra, K. L., 1990. "Improvements on strong uniform consistency of some known kernel estimates of a density and its derivatives," Statistics & Probability Letters, Elsevier, vol. 9(2), pages 133-140, February.
    • Handle: RePEc:eee:stapro:v:9:y:1990:i:2:p:133-140
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    Cited by:

    1. Clarke, Brenton R. & Futschik, Andreas, 2007. "On the convergence of Newton's method when estimating higher dimensional parameters," Journal of Multivariate Analysis, Elsevier, vol. 98(5), pages 916-931, May.
    2. Salim Bouzebda & Mohamed Chaouch & Sultana Didi Biha, 2022. "Asymptotics for function derivatives estimators based on stationary and ergodic discrete time processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(4), pages 737-771, August.
    3. R. Karunamuni & K. Mehra, 1991. "Optimal convergence properties of kernel density estimators without differentiability conditions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 43(2), pages 327-346, June.
    4. Christian Hesse, 1995. "Deconvolving a density from contaminated dependent observations," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 47(4), pages 645-663, December.

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