Inverse distance weighting is a common way of interpolating values zj at scattered data points Xj in Rn:
idw(P) = Σ wj zj / Σ wj
wj = f( |P - Xj| )
f(d) = 1 / dp
Is there a "best" p, for say
Xj uniformly distributed in the unit cube
and z(X) = cos( c . X ) + normal noise ?
(For that matter, is there a rationale for 1/d at all -- why not say Gaussian ?)
The Wikipedia article say that IDW minimizes a φ(x,u) which looks like least squares minimization with variance ~ distancep: maybe a connection to least squares, maybe not.
(Please add tag "interpolation", thanks.)