Journal of Statistical Planning and Inference 136 (2006) 2606 – 2629 www.elsevier.com/locate/jspi Statistical inference for location and scale of elliptically contoured models with monotone missing data A. Batsidis, K. Zografos ∗ Department of Mathematics, University of Ioannina, 451 10 Ioannina, Greece Received 30 January 2003; accepted 20 October 2004 Available online 8 December 2004 Abstract In this paper statistical inference is developed for the estimation and testing problems of the location and scale parameters of the elliptically contoured family of distributions. The data matrix is of a monotone missing pattern. The analytic form of the maximum likelihood estimators of location and scale are derived, and based on them, the likelihood ratio test statistics are obtained for testing the following: (i) the location and scale parameters are, separately, equal to a specified vector and matrix, (ii) the location and scale parameters are, simultaneously, equal to a specified vector and matrix, and (iii) the hypothesis of lack of correlation between sets of variates that jointly described by the elliptically contoured family of distributions. The test of sphericity is also derived in the particular case of the multivariate normal distribution. The asymptotic null distributions of the resulting test statistics are derived for k = 2, as well as, for k> 2 steps of monotone missing data. The results are illustratively applied in the Appendix A, to specific elliptically contoured models like the multivariate t-distribution. The results are also illustrated using simulated data from a multivariate t-distribution. © 2004 Elsevier B.V.All rights reserved. MSC: 62H12; 62H15; 62D05 Keywords: Monotone missing data; Elliptically contoured distributions; Estimation; Testing hypotheses; Lack of correlation; Multivariate t-distribution; Pearson type II and VII distributions ∗ Corresponding author. Tel.: +30 2651 098257; fax: +30 2651 098207. E-mail address: kzograf@cc.uoi.gr (K. Zografos). 0378-3758/$ - see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.jspi.2004.10.021