A note on application of kernel derivatives in density estimation with the univariate case

This paper considers the application of kernel density derivatives to real life data. Kernel density derivatives estimation is very fundamental and critical in statistical data analysis especially for exploratory and visualization purposes. As a result of the wide range of its applications, appropriate estimation of the kernel derivatives from its function and locating some statistical features such as bumps and modes of a set of observation is of a great importance. We consider the first and second derivative of the Gaussian kernel and compare their results in terms of performance using asymptotic mean integrated squared error as the error criterion function. The results of the comparison shows that as the derivative of the kernel function increases, the AMISE decreases with an increase in the smoothing parameter.