The Allan variance is a well-known estimator of frequency stability and is often used to classify a time series into one of the standard clock noise types. By identifying the power-law model for clock noise with its long-memory equivalent, the Allan variance can also serve as an estimate for the long-memory parameter. Although the Allan variance is not a maximum likelihood estimator, it can be ...

Wavelets have recently been a subject of great interest in geophysics, mathematics and signal processing. The discrete wavelet transform can be used to decompose a time series with respect to a set of basis functions, each one of which is associated with a particular scale. The properties of a time series at different scales can then be summarized by the wavelet variance, which decomposes the v...

We consider a random walk ( Z (1) n , · · · , Z n ) ∈ Z with the constraint that each coordinate of the walk is at distance one from the following one. In this paper, we show that this random walk is slowed down by a variance factor σ K = 2 K+2 with respect to the case of the classical simple random walk without constraint.

We introduce a partial order, variance majorization, on R, which is analogous to the majorization order. A new class of monotonicity inequalities, based on variance majorization and analogous to Schur convexity, is developed.

We propose a method for extending a given asset pricing formula to account for two additional sources of risk: the risk associated with future changes in market–calibrated parameters and the remaining risk associated with idiosyncratic variations in the individual assets described by the formula. The paper makes simple and natural assumptions for how these risks behave. These extra risks should...

Concerning a single major league at bat, the percentage of variance in batting performance attributable to skill differentials among major league baseball players can be calculated statistically. The statistically appropriate calculation is seriously discrepant with intuitions about the influence of skill in batting performance. This paradoxical discrepancy is discussed in terms of habits of th...

The reverberation time is a key feature for describing the acoustic properties of a reverberant room. It can be computed from a measured Room Impulse Response but in many applications it has to be estimated blindly. Existing blind methods give accurate estimates but they often exhibit high variance across different speakers. In this paper, a low variance blind estimator of the reverberation tim...

conjecture Jan Cameron ∗, Erik Christensen †, Allan M. Sinclair ‡,Roger R. Smith §,Stuart White ¶,Alan D. Wiggins ‖ ∗Department of Mathematics, Vassar College, Poughkeepsie, NY 12604, U.S.A.,†Institute for Mathematiske Fag, University of Copenhagen, Copenhagen, Denmark.,‡School of Mathematics, University of Edinburgh, JCMB, King’s Buildings, Mayfield Road, Edinburgh, EH9 3JZ, Scotland.,§Departm...

Allan variance method is a useful tool for analyzing the random errors, but the confidence on the estimate would be lower when the data length became shorter, therefore the modified Allan variance is deduced to analysis the random errors of MEMS inertial sensors (MINS). The definition and limitation of Allan variance are presented first, and then the modified Allan variance is deduced. Allan va...