Generalized Maximum Spacing Estimators

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 can be derived from an approximation based on simple spacings of the Kullback-Leibler information. In the present paper, we introduce a class of estimation methods, derived from approximations based on mth order spacings of certain information measures, i.e. the ^-divergences introduced by Csiszâr (1963). The introduced class of methods includes the MSP method as a special case. A subclass of these methods was considered earlier in Ranneby and Ekström (1997), i.e. those based on first order spacings. Here i t is found that such methods can be improved by using high order spa cings. We al so show that the suggested methods give consistent estimates under general conditions. 1