I discuss a novel technique for periodically extending by reflection an ordered series of phase-difference {xk.} to yield estimation of new frequency and time variances having improved longterm confidence and the same mean as the Allan variance. In addition, I describe a correction to a negative bias in the sample variance based on the actual number of observations in the measurements at long t...

The phase-noise spectrum determines the Allan variance by a well-known integral formula. It is shown here that unique inversion of this formula is not possible in general because the mapping from spectrum to Allan variance is not one-to-one. A necessary and sufficient condition for two distinct phase spectra to have the same Allan variance is given.

The authors consider the problem of estimating, under quadratic loss, the mean of a spherically symmetric distribution when its norm is supposed to be known and when a residual vector is available. They give a necessary and sufficient condition for the optimal James-Stein estimator to dominate the usual estimator. Various examples are given that are not necessarily variance mixtures of normal d...

In this paper we propose a methodology for minimizing the variance of a cube (mosaicked) representation of a scene imaged by a pan-tilt camera. The minimization is based on the estimation of the vignetting image distortion, using the pan and tilt degrees of freedom instead of color calibrating patterns. Experiments with real images show that variance minimization is effective for improving even...

In this article we discuss estimation of the common variance of several normal populations with tree order restricted means. We discuss the asymptotic properties of the maximum likelihood estimator of the variance as the number of populations tends to infinity. We consider several cases of various orders of the sample sizes and show that the maximum likelihood estimator of the variance may or m...