  Vertically weighted averages perform a bilateral filtering of data, in order
to preserve fine details of the underlying signal, especially discontinuities
such as jumps (in dimension one) or edges (in dimension two). In homogeneous
regions of the domain the procedure smoothes the data by averaging nearby data
points to reduce the noise, whereas in inhomogenous regions the neighboring
points are only taken into account when their value is close to the current
one. This results in a denoised reconstruction or estimate of the true signal
without blurring finer details.
  This paper addresses the lack of results about the construction and
evaluation of confidence intervals based on the vertically weighted average,
which is required for a proper statistical evaluation of its estimation
accuracy. Based on recent results we discuss and investigate in greater detail
fixed sample as well as fixed width (conditional) confidence intervals
constructed from this estimator. The fixed width approach allows to specify
explicitly the estimator's accuracy and determines a random sample size to
ensure the required coverage probability. This also fixes to some extent the
inherent property of the vertically weighted average that its variability is
higher in low-density regions than in high-density regions. To estimate the
variances required to construct the procedures, we rely on resampling
techniques, especially the bootstrap and the jackknife.
  Extensive Monte Carlo simulations show that the proposed confidence intervals
are reliable in terms of their coverage probabilities for a wide range of
parameter settings.
