A note on the maximum likelihood estimators for the location and scatter parameters of a multivariate Cauchy distribution

ARSLAN O., Kent J.

COMMUNICATIONS IN STATISTICS-THEORY AND METHODS, cilt.27, sa.12, ss.3007-3014, 1998 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 27 Sayı: 12
  • Basım Tarihi: 1998
  • Doi Numarası: 10.1080/03610929808832269
  • Dergi Adı: COMMUNICATIONS IN STATISTICS-THEORY AND METHODS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.3007-3014
  • Anahtar Kelimeler: Cauchy distribution, robustness, maximum likelihood estimator, EM algorithm, iterative reweighting algorithm, EM ALGORITHM, T-DISTRIBUTION
  • Ankara Üniversitesi Adresli: Hayır

Özet

The likelihood function of a multivariate Cauchy distribution with unknown location and scatter parameters in p 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). fn this paper, we show that when n = p + 1, the maximum of the location-scatter Cauchy likelihood function occurs when the parameters lie on a p-dimensional surface.