We attempt to derive concentration results for denoiser loss
estimators, with the aim of using the loss estimators to select the
best value of the window size $k$ to be used with the Discrete 
Universal Denoiser (DUDE) to denoise a given sequence. We show that
for a loss-estimator proposed in the literature, it is not possible to
derive strong concentration results for certain pathological input
seqeunces. By modifying the estimator slightly we obtain a loss
estimator for which the DUDE's estimated loss concentrates around the
true loss as long as $kM^k = o(n)$, where $M$ is the size of the
alphabet and $n$ the sequence length. We also show that for certain
non-pathological clean sequences, it is possible to derive
concentration results for $k \ge \log n$.