Linear Mixed Models using Skew-Normal/Independent Distributions:
Estimation and Influence analysis.
Abstract:
The   linear mixed models is discussed under skew-normal/independent
distribution. This class provides a useful generalization of normal (and
skew-normal)linear mixed models since it is assumed that the random
effects and the random error terms follow jointly a multivariate
skew-normal/independent distribution.  Inspired by the EM algorithm  that
is  used   to obtain   the   maximum likelihood   estimates,  a  study
influence analysis for linear mixed models is developed, following  the
approach   of  Zhu et al. (2001) and   Zhu and Lees (2001).
The influence of observations on statistical inference is of importance in
statistical data analysis. A practical and well-established approach to
influence analysis is based on case deletion (Cook, 1977; Zhu et al.,
2001),  a  general approach was   proposed  by    Cook (1986) and Zhu and
Lees (2001, that   is  known  as  the   local   influence   method.
Finally, a real data set has been analyzed in order to illustrate the
usefulness of the proposed methodology.