Estimation of the Scaling Parameter for a Kernel-Type Density Estimate

An algorithm is given for estimation of the scaling parameter Λ in the kernel-type density estimate derived from the Fourier integral. A Monte Carlo study of five different densities compares the integrated square error (ISE) for the resulting estimate to the ISE for the Fourier integral estimate (FIE) with mean integrated squared error (MISE) optimal Λ and to the ISE for the normal kernel with asymptotically MISE optimal Λ. The study shows the FIE with estimated Λ compares favorably with the other estimates and demonstrates the asymptotic optimality of the FIE for smooth densities.