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In some applications it is necessary to estimate derivatives of probabilitydensities defined on the positive semi-axis. The quality of nonparametricestimates of the probability densities and their derivatives are stronglyinfluenced by smoothing parameters (bandwidths). In this paper an expressionfor the optimal smoothing parameter of the gamma kernel estimate of the densityderivative is obtained. For this parameter data-driven estimates based onmethods called "rule of thumb" and "cross-validation" are constructed. Thequality of the estimates is verified and demonstrated on examples of densityderivatives generated by Maxwell and Weibull distributions.

Data-driven bandwidth choice for gamma kernel estimates of density derivatives on the positive semi-axis