Generalized Maximum Spacing Estimation for Multivariate Observations

In this paper, the maximum spacing method is considered for multivariate observations. Nearest neighbour balls are used as a multidimensional analogue to univariate spacings. A class of information-type measures is used to generalize the concept of maximum spacing estimators. Weak and strong consistency of these generalized maximum spacing estimators are proved both when the assigned model class is correct and when the true density is not a member of the model class. An example of the generalized maximum spacing method in model validation context is discussed.