Skew-Normal Distribution in Multivariate Null Intercept Measurement Error Model

In this paper we discuss inferential aspects of the multivariate null intercept measurement error model where the unobserved value of the covariate (latent variable) follows a skew-normal distribution. First, closed form expressions of the marginal likelihood, the score function and the observed information matrix of the observed quantities are presented allowing direct inference implementation. Then, we indicate how maximum likelihood estimators of the parameter vector may be obtained via the ECM algorithm. Additionally, an EM-type algorithm for evaluating the restricted maximum likelihood estimate under equality constraints on the regression coe±cients is examined. In order to discuss some diagnostic techniques in this type of models, we derive the appropriate matrices to assess the local in°uence on the parameters estimate under di®erent perturbation schemes. The results and methods are applied to a dental clinical trial presented in Hadgu and Koch (1999).