Radius selection using kernel density estimation for the computation of nonlinear measures

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