Window occupancy for an equally spaced regression design ($N_x\ge \frac{n}{4}\min (h,1)$)

Let $x_i=i/n$, $1\le i\le n$, and let $N_x$ count sites within distance $h/2$ of $x\in [0,1]$. If $nh\ge 2$, a nearest site lies in the closed window, so $N_x\ge 1$. A clipped window has length at least $\min (h,1)/2$, and a grid count gives $N_x\ge n\min (h,1)/2-1$. Combining these two bounds yields $N_x\ge n\min (h,1)/4$. For $0<h\le 2$, the stronger clipped-length bound $h/2$ directly gives $N_x\ge \lfloor nh/2\rfloor \ge nh/4$. These estimates include both endpoints of the domain.