Effect of the initial estimator on the asymptotic behavior of one-step M-estimator |
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| Authors: | Jana Jurečková Pranab Kumar Sen |
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| Institution: | (1) Department of Probability and Mathematical Statistics, Charles University, Sokolovská 83, 186 00 Progue 8, Czechoslovakia;(2) Department of Biostatistics 201 H, University of North Carolina at Chapel Hill, 27514 Chapel Hill, NC, U.S.A. |
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| Abstract: | For a general (real) parameter, let M
nbe the M-estimator and M
n
(1) be its one-step version (based on a suitable initial estimator M
n
(0)). It is known that, under certain regularity conditions, n(M
n
(1)-M
n)=O
p(1). The asymptotic distribution of n(M
n
(1)-M
n) is studied; it is typically non-normal and it reveals the role of the initial estimator M
n
(0).Work of this author was partially supported by the Office of Naval Research, Contract No. N00014-83-K-0387 |
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| Keywords: | Influence function M-estimator one-step version of M-estimator random change of time score function weak convergence of M-processes |
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