Strong consistency of the jackknife estimate of variance and covariance for Koziol-Green integrals

Abstract

In this paper we establish almost sure consistency of the jackknife estimate of variance and covariance for Koziol–Green integrals. These are asymptotically Gaussian estimates of the form , where we put for the MLE of the distribution function under the Koziol-Green proportional censorship model. Confidence sets for functions of general integrals may be constructed from our results.

AMS Classifications::

• 62G09 (Resampling methods)
• 62G20 (Asymptotic-properties)

Keywords:

• Jackknife
• Koziol-Green model
• Proportional censorship

Work supported by the DGES grant PB98-0182-C02–02.

Work supported by the DGES grant PB98-0182-C02–02.

Notes

Work supported by the DGES grant PB98-0182-C02–02.