Saddlepoint approximations and tests based on multivariate M-estimates
- Robinson, J. University of Sydney
- Ronchetti, Elvezio Istituto di finanza (IFin), Facoltà di scienze economiche, Università della Svizzera italiana, Svizzera
- Young, G. A. University of Cambridge
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2003
Published in:
- The Annals of Statistics. - Institute of Mathematical Statistics. - 2003, vol. 31, no. 4, p. 1154-1169
English
We consider multidimensional M-functional parameters defined by expectations of score functions associated with multivariate M-estimators and tests for hypotheses concerning multidimensional smooth functions of these parameters. We propose a test statistic suggested by the exponent in the saddlepoint approximation to the density of the function of the M-estimates. This statistic is analogous to the log likelihood ratio in the parametric case. We show that this statistic is approximately distributed as a chi-squared variate and obtain a Lugannani-Rice style adjustment giving a relative error of order n-1. We propose an empirical exponential likelihood statistic and consider a test based on this statistic. Finally we present numerical results for three examples including one in robust regression.
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- English
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- Economics
- Other electronic version
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- RERO DOC 7819
- ARK ark:/12658/srd1317931
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- https://n2t.net/ark:/12658/srd1317931
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