  Direct evaluation of the rate-distortion function has rarely been achieved
when it is strictly greater than its Shannon lower bound. In this paper, we
consider the rate-distortion function for the distortion measure defined by an
epsilon-insensitive loss function. We first present the Shannon lower bound
applicable to any source distribution with finite differential entropy. Then,
focusing on the Laplacian and Gaussian sources, we prove that the
rate-distortion functions of these sources are strictly greater than their
Shannon lower bounds and obtain analytically evaluable upper bounds for the
rate-distortion functions. Small distortion limit and numerical evaluation of
the bounds suggest that the Shannon lower bound provides a good approximation
to the rate-distortion function for the epsilon-insensitive distortion measure.
