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Another look at the jackknife: further examples of generalized bootstrap

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  • Chatterjee, Snigdhansu

Abstract

In this paper we have three main results. (a) We show that all jackknife schemes are special cases of generalised bootstrap. (b) We introduce a new generalised bootstrap technique called DBS to estimate the mean-squared error of the least-squares estimate in linear models where the number of parameters tend to infinity with the number of data points, and the error terms are uncorrelated with possibly different variances. Properties of this new resampling scheme are comparable to those of UBS introduced by Chatterjee (1997, Tech. Report No. 2/97, Calcutta). (c) We show that delete-d jackknife schemes belong to DBS or UBS depending on the limit of n-1d. We also study the second-order properties of jackknife variance estimates of the least-squares parameter estimate in regression.

Suggested Citation

  • Chatterjee, Snigdhansu, 1998. "Another look at the jackknife: further examples of generalized bootstrap," Statistics & Probability Letters, Elsevier, vol. 40(4), pages 307-319, November.
    • Handle: RePEc:eee:stapro:v:40:y:1998:i:4:p:307-319
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    References listed on IDEAS

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    1. Bera, Anil K & Higgins, Matthew L, 1993. "ARCH Models: Properties, Estimation and Testing," Journal of Economic Surveys, Wiley Blackwell, vol. 7(4), pages 305-366, December.
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    1. Minyong Kang & Chang Wook Jeong & Woo Suk Choi & Yong Hyun Park & Sung Yong Cho & Sangchul Lee & Seung Bae Lee & Ja Hyeon Ku & Sung Kyu Hong & Seok-Soo Byun & Hyeon Jeong & Cheol Kwak & Hyeon Hoe Kim , 2014. "Pre- and Post-Operative Nomograms to Predict Recurrence-Free Probability in Korean Men with Clinically Localized Prostate Cancer," PLOS ONE, Public Library of Science, vol. 9(6), pages 1-7, June.
    2. De Vos, Ignace & Stauskas, Ovidijus, 2021. "Bootstrap Improved Inference for Factor-Augmented Regressions with CCE," Working Papers 2021:16, Lund University, Department of Economics.

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