Kernel density estimation - different choice of kernel

Question

There are many choices of kernel function to use in kernel density estimation:

• Gaussian,
• Epanechnikov,
• Uniform,
• Triangular,
• and so on.

I'm using Gaussian kernel to estimate density of two-dimensional spatial point pattern in my paper and there is reviewer that questions me whether can I justify my choice rather than letting it be an arbitrary choice "because Gaussian (kernel) is already widely known".

Is the choice of kernel function completely arbitrary (and bandwidth is all that matters), or is there a logical justification for selecting specific kernel function?

Answer 1

If I remember well, the Epanechnikov has some optimality properties for interior points, at least in one dimension, while the triangular one is optimal at the boundary. A good and thorough reference will be the book by Fan, J. and Gijbels, I. (1996) Local Polynomial Modelling and its Applications (341pp). Chapman and Hall

Now in general, the choice of the kernel plays only a small role compared to the choice of the bandwidth, which can radically change your estimates. This is probably where you ought to convince your referee.