Maximum Spacing Estimates Based oil Different Metrics

The maximum spacing (MSP) method, introduced by Cheng and Amin (1983) and independently by Ranneby (1984), is a general method for estimating param­ eters in univariate continuous distributions and is known to give consistent and asymptotically efficient estimates under general conditions. This method, which is closely related to the maximum likelihood (ML) method, can be derived from an approximation based on simple spacings of the Kullback-Leibler information. In the present paper, the ideas behind the MSP metod axe extended and a class of estimation methods is derived from approximations of certain information mea­ sures, i.e. the -̂divergences introduced by Csiszâr (1963). We call these methods generalized maximum spacing (GMSP) methods, and it will be shown under gen­ eral conditions that they give consistent estimates. GMSP methods have the advantage that they work also in situations where the ML method breaks down, e.g. due to an unbounded likelihood function. Other properties, such as asymp­ totic normality and the behaviour of the estimates when the assigned model is only approximately true, will be discussed.1