''Constructive wavelet networks'' are investigated as a universal tool
for function approximation. The parameters of such networks are obtai
ned via some ''direct'' Monte-Carlo procedures. Approximation bounds a
re given. Typically, it is shown that such networks with one layer of
''wavelons'' achieve an L(2)-error of order O(N--rho/d), where N is th
e number of nodes, d is the problem dimension and rho is the number of
summable derivatives of the approximated function, An algorithm is al
so proposed to estimate this approximation based on noisy input-output
data observed from the function under consideration. Unlike neural ne
twork training, this estimation procedure does not rely on stochastic
gradient type techniques such as the celebrated ''backpropagation,'' a
nd it completely avoids the problem of poor convergence or undesirable
local minima.