Multivariate Probability Integral Transformation: Application to maximum likelihood estimation

摘要

Let (X_1, X_2) be a continuous random vector with a cdf F. The probability integral transformation (pit) is the univariate random variable P_2 = F(X_1,X_2). The expression of its cdf and a simulation algorithm in terms of the quantile function given by Chakak et al [2000], when the distribution is absolutely continuous, are extended for distributions that may present singularity. Maximum likelihood estimation of the dependence parameter based on the pit is investigated by simulation. It is shown to perform well for singular families of distributions. Extension to higher dimensions is considered.