AN ASYMPTOTICALLY OPTIMAL HISTOGRAM SELECTION RULE

A random sample is available from a multivariate distribution having a bounded density, which is assumed to satisfy a mild additional condition. A finite collection of histogram estimates of the unknown density is constructed, whose cardinality increases algebraically fast with respect to the size of the random sample. A histogram selection rule is introduced, which is shown to be asymptotically optimal relative to integrated squared error loss. This research was supported in part by National Science Foundation Grant MCS83-01 257. AMS 1980 subject classifications. Primary 62G30; secondary 62G99.