A universally acceptable smoothing factor for kernel density estimates

We define a minimum distance estimate of the smoothing factor for kernel density estimates, based on a methodology first developed by Yatracos. It is shown that if fₙₕ denotes the kernel density estimate on Rᵈ for an i.i.d. sample of size n drawn from an unknown density f, where h is the smoothing factor, and if fₙ is the kernel estimate with the same kernel and with the proposed new data-based smoothing factor, then, under a regularity condition on the kernel K, f n → ∞ E ∫ | fₙ - f|dxinfh>0 E ∫ |fₙₕ - f|dx ≤ 3. This is the first published smoothing factor that can be proven to have this property.