Improvement on Some Known Nonparametric Uniformly Consistent Estimators of Derivatives of a Density

Based on a random sample from a univariate distribution with density f, this note exhibits a class of kernel estimators of the pth order derivative f⁽ᵖ⁾ of f, p 0 fixed. These estimators improve some known estimators of f⁽ᵖ⁾ by weakening the conditions, sharpening the rates of convergence, or both for the properties of strong consistency, asymptotic unbiasedness and mean square consistency, each uniform on the real line.