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Delta and jackknife estimators with low bias for functions of binomial and multinomial parameters

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  • Withers, Christopher S.
  • Nadarajah, Saralees

Abstract

An estimator is said to be of orders>0 if its bias has magnitude n−s, where n is the sample size. We give delta estimators and jackknife estimators of order four for smooth functions of the parameters of a multinomial distribution. An unbiased estimator is given for its density function. We also give a jackknife estimator of any order for smooth functions of the binomial parameter.

Suggested Citation

  • Withers, Christopher S. & Nadarajah, Saralees, 2013. "Delta and jackknife estimators with low bias for functions of binomial and multinomial parameters," Journal of Multivariate Analysis, Elsevier, vol. 118(C), pages 138-147.
    • Handle: RePEc:eee:jmvana:v:118:y:2013:i:c:p:138-147
    DOI: 10.1016/j.jmva.2013.02.006
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    References listed on IDEAS

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    1. Murray Jorgensen, 2004. "Using Multinomial Mixture Models to Cluster Internet Traffic," Australian & New Zealand Journal of Statistics, Australian Statistical Publishing Association Inc., vol. 46(2), pages 205-218, June.
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    Cited by:

    1. Zhang, Rui & Shonkwiler, J. Scott, 2017. "Bias Correction of Welfare measures in Non-Market Valuation: Comparison of the Delta Method, Jackknife and Bootstrap," 2017 Annual Meeting, July 30-August 1, Chicago, Illinois 258099, Agricultural and Applied Economics Association.
    2. Withers, Christopher S. & Nadarajah, Saralees, 2014. "Cumulants of multinomial and negative multinomial distributions," Statistics & Probability Letters, Elsevier, vol. 87(C), pages 18-26.

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    1. Withers, Christopher S. & Nadarajah, Saralees, 2014. "Cumulants of multinomial and negative multinomial distributions," Statistics & Probability Letters, Elsevier, vol. 87(C), pages 18-26.

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