= Window occupancy for an equally spaced regression design
{title2=$N_x\ge\frac n4\min(h,1)$}
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 $nh\ge2$, a nearest site lies in the closed window, so $N_x\ge1$. 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 $0<h\le2$, 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.
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