# Asymptotic normality of generalized maximum spacing estimators for multivariate observations

## TL;DR

This paper proves the asymptotic normality of generalized maximum spacing estimators for multivariate data using nearest neighbor balls, extending univariate concepts to higher dimensions.

## Contribution

It introduces a generalized class of maximum spacing estimators for multivariate observations and establishes their asymptotic normality under correct model assumptions.

## Key findings

- Asymptotic normality is established for the estimators.
- Nearest neighbor balls serve as a multidimensional analogue to univariate spacings.
- The results hold when the true density belongs to the model class.

## Abstract

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. Asymptotic normality of these generalized maximum spacing estimators is proved when the assigned model class is correct, that is the true density is a member of the model class.