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Sufficient bootstrapping

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  • Singh, Sarjinder
  • Sedory, Stephen A.

Abstract

In this paper, we introduce an idea we refer to as sufficient bootstrapping, which is based on retaining only distinct individual responses, and also develop a theoretical framework for the techniques. We demonstrate through numerical illustrations that the proposed sufficient bootstrapping may be better than the conventional bootstrapping in certain situations. The expected gain by the sufficient bootstrapping has been computed for small and large sample sizes. The relative efficiency shows that there could be significant gain by the sufficient bootstrapping and it could reduce computational burden. Variance expressions for both the conventional and sufficient bootstrapping sample means are derived. Here the word "sufficient" is being used in the sense that it is "sufficient to take just one of any duplicated items in the bootstrap sample" and is not tightly connected to sufficiency in terms of any likelihood perspective. R code for comparing bootstrapping and sufficient bootstrapping are provided. A huge scope of further studies is suggested.

Suggested Citation

  • Singh, Sarjinder & Sedory, Stephen A., 2011. "Sufficient bootstrapping," Computational Statistics & Data Analysis, Elsevier, vol. 55(4), pages 1629-1637, April.
    • Handle: RePEc:eee:csdana:v:55:y:2011:i:4:p:1629-1637
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    Citations

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    Cited by:

    1. Ufuk Beyaztas & Aylin Alin, 2014. "Sufficient jackknife-after-bootstrap method for detection of influential observations in linear regression models," Statistical Papers, Springer, vol. 55(4), pages 1001-1018, November.
    2. Sayed A. Mostafa & Ibrahim A. Ahmad, 2021. "Kernel Density Estimation Based on the Distinct Units in Sampling with Replacement," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(2), pages 507-547, November.
    3. Ufuk Beyaztas & Beste H. Beyaztas, 2019. "On Jackknife-After-Bootstrap Method for Dependent Data," Computational Economics, Springer;Society for Computational Economics, vol. 53(4), pages 1613-1632, April.

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