Bandwidth value for vector of equal values in kernel density estimation

Question

How to define the value of bandwidth when we have a vector where all the values is the same? In this case, IQR and sample variation are both equal zero and Silverman's rule also result in zero.

Using R, we have for $\vec{v} = (1,1)$ the bandwidth of 0.7835

density(c(1,1))$bw

and for $\vec{v} = (10,10)$, the value 7.834955

density(c(10,10))$bw

Answer 1

I found an way to deal with small values of $\sigma$ or $IQR$. I believe that this is what is used in the density function:

if $\sigma$ < $\epsilon$ or $IQR < \epsilon$ than $ bandwidth = 0.9 \bar{x} n^{-0.2} $

For $\vec{x} = (1,1)$, we get 0.7834955 like in

density(c(1,1))$bw

I used $\epsilon = 10^{-6}$