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A Berry-Esséen-type theorem of quantile density estimators

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  • Cheng, Cheng

Abstract

A Berry-Esséen-type theorem showing the near-optimal quality of the normal distribution approximation to the distribution of smooth quantile density estimators is established in this paper. Under more restrictive conditions on the smoothing kernel, an n-1/2-error bound Berry-Esséen result is established as well.

Suggested Citation

  • Cheng, Cheng, 1998. "A Berry-Esséen-type theorem of quantile density estimators," Statistics & Probability Letters, Elsevier, vol. 39(3), pages 255-262, August.
    • Handle: RePEc:eee:stapro:v:39:y:1998:i:3:p:255-262
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    References listed on IDEAS

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    1. Falk, Michael, 1986. "On the estimation of the quantile density function," Statistics & Probability Letters, Elsevier, vol. 4(2), pages 69-73, March.
    2. Cheng, Cheng, 1995. "The Bernstein polynomial estimator of a smooth quantile function," Statistics & Probability Letters, Elsevier, vol. 24(4), pages 321-330, September.
    3. Kaigh, W. D. & Sorto, Maria Alejandra, 1993. "Subsampling quantile estimator majorization inequalities," Statistics & Probability Letters, Elsevier, vol. 18(5), pages 373-379, December.
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    Cited by:

    1. Gabriel Montes Rojas & Andrés Sebastián Mena, 2020. "Density estimation using bootstrap quantile variance and quantile-mean covariance," Documentos de trabajo del Instituto Interdisciplinario de Economía Política IIEP (UBA-CONICET) 2020-50, Universidad de Buenos Aires, Facultad de Ciencias Económicas, Instituto Interdisciplinario de Economía Política IIEP (UBA-CONICET).

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