ABSTRACT This article considers maximum spacing (MSP) estimation for multivariate observations under model misspecification. A broad class of MSP estimators corresponding to different information‐type divergence measures is studied. This class also includes the MSP estimator corresponding to the Kullback‐Leibler information measure, obtained using the logarithmic function. It is shown that, under model misspecification, the MSP estimator converges to a well‐defined limit that depends on the chosen divergence measure; this establishes consistency. The behavior of MSP estimators under different divergence measures is explored through simulation studies. The asymptotic properties of MSP estimators and spacing functions are exploited to illustrate tools for detecting model misspecification in large samples.
Bao et al. (Mon,) studied this question.