My understanding of histogram density estimation: For $k$ predefined equal-width bins $(b_0, b_1], (b_1, b_2], ..., (b_{k-1}, b_k]$ and $n$ observations $x_1,...,x_n \in (b_0,b_k]$, we estimate density as $f(x) = \frac{1}{b_1-b_0} \sum_{i=1}^k P_k 1_{x\in (b_{i-1},b_i]}$, where $P_k$ is the proportion of observations falling in the $k^{th}$ bin.
This seems to me like parametric density estimation, with a fixed number $k$ of parameters $P_1,...,P_k$ (or just the first $k-1$), which does not grow with $n$. However, here and on other websites, I see histogram density estimation referred to as non-parametric. I've seen several definitions of "nonparametric" - which of those would include this method?
