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RKHS approach to detection and estimation problems-V: Parameter estimation

Using reproducing-kernel Hilbert space (RKHS) techniques, we obtain new results for three different parameter estimation problems. The new results are 1) an explicit formula for the minimum-variance unbiased estimate of the arrival time of a step function in white Gaussian noise, 2) a new interpretation of the Bhattacharyya bounds on the variance of an unbiased estimate of a function of regression coefficients, and 3) a concise formula for the Cramer-Rao bound on the variance of an unbiased estimate of a parameter determining the covariance of a zero-mean Gaussian process.