  When nonlinear measures are estimated from sampled temporal signals with
finite-length, a radius parameter must be carefully selected to avoid a poor
estimation. These measures are generally derived from the correlation integral
which quantifies the probability of finding neighbors, i.e. pair of points
spaced by less than the radius parameter. While each nonlinear measure comes
with several specific empirical rules to select a radius value, we provide a
systematic selection method. We show that the optimal radius for nonlinear
measures can be approximated by the optimal bandwidth of a Kernel Density
Estimator (KDE) related to the correlation sum. The KDE framework provides
non-parametric tools to approximate a density function from finite samples
(e.g. histograms) and optimal methods to select a smoothing parameter, the
bandwidth (e.g. bin width in histograms). We use results from KDE to derive a
closed-form expression for the optimal radius. The latter is used to compute
the correlation dimension and to construct recurrence plots yielding an
estimate of Kolmogorov-Sinai entropy. We assess our method through numerical
experiments on signals generated by nonlinear systems and experimental
electroencephalographic time series.
