Summary We present consistency results for estimators of the box-counting dimension of the support of probability distributions. The box-counting dimension of the support E is defined via the covering number, i.e. the minimal cardinality of a cover of E consisting of cubes of fixed side-length....

We study the loss of information (measured in terms of the Kullback-Leibler distance) caused by observing "grouped" data (observing only a discretized version of a continuous random variable). We analyze the asymptotical behaviour of the loss of information as the partition becomes finer. In the...