# What are good references on calculating confidence intervals using subsampling or the delete-d jackknife?

I searched for references on using subsampling or the delete-d jackknife to calculate confidence intervals but wasn't able to find much.

Could someone please offer more reference on using subsampling or the delete-d jackknife to calculate confidence intervals?

The practice in the field seems to be to rely on asymptotic normality of the estimate and to use the jackknife just as an estimate of variance to help calculate standard errors, which are then plugged into a hoped-for normal distribution of the estimate.

If there's reason to think the estimate doesn't have a normal distribution I think a bootstrap of some sort is more appropriate eg for asymmetric confidence intervals.

Some references on using delete-d-jackknife to estimate variance include these articles by Messer and Gamst, Shao and Wu, and Xiquan Shi. If you are interested in delete-a-group-jackknife (basically a stratified version) then there is a bunch of articles by Kott including (from the help files for Zardetto's EVER library):

Kott, Phillip S. (1998) "Using the Delete-A-Group Jackknife Variance Estimator in NASS Surveys", RD Research Report No. RD-98-01, USDA, NASS: Washington, DC.

Kott, Phillip S. (1999) "The Extended Delete-A-Group Jackknife". Bulletin of the International Statistical Instititute. 52nd Session. Contributed Papers. Book 2, pp. 167-168.

Kott, Phillip S. (2001) "The Delete-A-Group Jackknife". Journal of Official Statistics, Vol.17, No.4, pp. 521-526.

For subsampling you can look at material in my book or Efron and Tibshirani. But the best reference that has been over looked so far is the book by Politis, Romano and Wolf. The original work on this predates the bootstrap and is due mainly to Hartigan in his 1969 paper in JASA. Here are links to the books.

Subsampling

Bootstrap Methods: A Guide for Practitioners and Researchers

An Introduction to the Bootstrap