(5.19) |

The right hand side depends on . Note that can be estimated by (binomial distribution). If we substitute this estimate, the equation becomes equivalent to Ellner's. However, this substitution is not justified from a statistical point of view (in fact, one uses information from distances !). The dimension can be estimated by numerical maximization of the (log-) likelihood function (or by iteration on eq. (5.20) [Kendall and Stuart, 1979, §32.17A]). The variance is given by ( is fixed):

which is larger than (5.18), except when , when the Takens, Ellner and ``doubly truncated'' estimators and their variances become the same.