We derive unique Karcher means for symmetric probability distributions on the unit circle, under the conditions that: (i) the distributions have differentiable density functions and (ii) the distributions are concentrated at the symmetry points.

We present a novel methodology for a comprehensive statistical analysis of approximately periodic biosignal data. There are two main challenges in such analysis: (1) the automatic extraction (segmentation) of cycles from long, cyclostationary biosignals and (2) the subsequent statistical...

Constructing generative models for functional observations is an important task in statistical functional analysis. In general, functional data contains both phase (or x or horizontal) and amplitude (or y or vertical) variability. Traditional methods often ignore the phase variability and focus...

Many applications call for measuring the response due to shocks from several variables at once. We introduce a joint impulse response function (jIRF) that is independent of the order of the variables and allows for simultaneous shocks from multiple variables in the VAR rather than one at a time...