Small Sample Asymptotic Expansions for Multivariate $M$-Estimates
Open Access
- 1 September 1982
- journal article
- Published by Institute of Mathematical Statistics in The Annals of Statistics
- Vol. 10 (3) , 672-689
- https://doi.org/10.1214/aos/1176345864
Abstract
Asymptotic expansions are derived for the densities of multivariate $M$-estimates. The expansion is based on a saddlepoint technique and yields good accuracy in the tails for small sample sizes. Numerical results are given for robust estimation of location and scale and these are compared with known Monte Carlo results.Keywords
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