Assuming Distance_Unique, Distance, etc. are all matrices or vectors and not functions, the two inner loops are certainly not required. I also assumed you've predeclared your Summation_Residual_Squared vector to avoid growing it in the loop.
Summation_Residual_Squared = zeros(size(Distance_Unique));
for duidx = 1:numel(Distance_Unique)
Residual_Sqrd = Residual_Squared(Distance_Unique(duidx) == Distance);
Summation_Residual_Squared(duidx) = sum(Residual_Sqrd(:));
end
