论文信息 - A note on the maximum likelihoood estimators for the location and scatter parameters of a multivariate cauchy distribution

A note on the maximum likelihoood estimators for the location and scatter parameters of a multivariate cauchy distribution

The likelihood function of a multivariate Cauchy distribution with unknown location and scatter parameters in ρ dimensions has a unique maximum provided the sample is in general position and is of size n > p + 1 (see Kent and Tyler 1991 and Kent et al., 1994). In this paper, we show that when n=p+l, the maximum of the locationscatter Cauchy likelihood function occurs when the parameters lie on a ρ–dimensional surface.

Olcay Arslan | John T. Kent | J. Kent | O. Arslan

[1] James A. Reeds,et al. Asymptotic Number of Roots of Cauchy Location Likelihood Equations , 1985 .

[2] V. Barnett. Evaluation of the maximum-likelihood estimator where the likelihood equation has multiple roots. , 1966, Biometrika.

[3] J. Kent,et al. Convergence Behavior of the em algorithm for the multivariate t -distribution , 1995 .

[4] New York Dover,et al. ON THE CONVERGENCE PROPERTIES OF THE EM ALGORITHM , 1983 .

[5] J. B. Copas,et al. On the unimodality of the likelihood for the Cauchy distribution , 1975 .

[6] David E. Tyler,et al. Maximum likelihood estimation for the wrapped Cauchy distribution , 1988 .

[7] Gorm Gabrielsen,et al. On the unimodality of the likelihood for the Cauchy distribution: Some comments , 1982 .

[8] David E. Tyler,et al. Redescending $M$-Estimates of Multivariate Location and Scatter , 1991 .

[9] D. Rubin,et al. Maximum likelihood from incomplete data via the EM - algorithm plus discussions on the paper , 1977 .

[10] David E. Tyler,et al. A curious likelihood identity for the multivariate t-distribution , 1994 .

[11] Xiao-Li Meng,et al. The EM Algorithm—an Old Folk‐song Sung to a Fast New Tune , 1997 .