Maximum-likelihood estimation for the multivariate Sarmanov distribution: simulation study

Used to model dependency in a multivariate setting with given marginals, Sarmanov's family of distributions creates difficulties when it comes to statistical inference. In this paper, we study maximum-likelihood procedures for estimating Sarmanov's distribution parameters for two different models: Under model I, we make use of a random data sample of volume m observed from an n-dimensional random vector, while model II consists of the first n dependent univariate random variables from a discrete-time stochastic process to which we try to fit Sarmanov's distribution starting from the corresponding n-tuple of observed values. To estimate some specific parameters, the use of the method of moments based on the covariance/correlation coefficient is also suggested. We illustrate these methods on simulated data and discuss the results.