###
ONE-STEP JACKKNIFE FOR M-ESTIMATORS COMPUTED

USING NEWTON'S METHOD

###
JUN SHAO

*Department of Mathematics, University of Ottawa,*

585 King Edward, Ottawa, Ontario, Canada K1N 6N5
(Received October 4, 1991; revised February 6, 1992)

**Abstract.**
To estimate the dispersion of an M-estimator computed
using
Newton's iterative method, the jackknife method usually requires to repeat the
iterative process *n* times, where *n* is the sample size. To simplify the
computation, one-step jackknife estimators, which require no iteration, are
proposed
in this paper. Asymptotic properties of the one-step jackknife estimators are
obtained under some regularity conditions in the i.i.d. case and in a linear or
nonlinear model. All the one-step jackknife estimators are shown to be
asymptotically equivalent and they are also asymptotically equivalent to the
original jackknife estimator. Hence one may use a dispersion estimator whose
computation is the simplest. Finite sample properties of several one-step
jackknife
estimators are examined in a simulation study.

*Key words and phrases*:
Asymptotic equivalence, asymptotic
variance,
computation of jackknife estimator, consistency, iteration, M-estimator,
one-step
estimator.

**Source**
( TeX ,
DVI ,
PS )