On Computation of Efficiency of Maximum-Likelihood Estimate When Observing a Discontinuous Signal in White Noise

In observing a discontinuous signal in white Gaussian noise with a spectral density of $\varepsilon^2$ the mean-square risk of the best estimate of the shift parameter for $\varepsilon\to\infty$ is of magnitude $C\varepsilon^4/r^4+o(\varepsilon^4)$, where $r^2$ is the sum of the squares of the signal jumps. In this paper, identities linking the quadratic risks of equivariant estimates are used to find the value of the constant $C$.