Several widely used tests for a changing mean exhibit nonmonotonic power in finite samples due to “incorrect” estimation of nuisance parameters under the alternative. In this paper, we study the issue of nonmonotonic power in testing for changing mean. We investigate the asymptotic power properties of the tests using a new framework where alternatives are characterized as having “large” changes...

We present Power Mean Pyramid Scores (PMP), an evaluation metric that extends the Pyramid evaluation scheme for summarization by combining Sentence Content Units (SCU) scores using Power Mean. The Pyramid method generates a summarization score by linearly combining component SCU scores. We find that by combining SCU scores using Power Mean, we can optimize a single parameter, α, leading to sign...

We study the motion of an n-dimensional closed spacelike hypersurface in a Lorentzian manifold in the direction of its past directed normal vector, where the speed equals a positive power p of the mean curvature. We prove that for any p ∈ (0, 1], the flow exists for all time when the Ricci tensor of the ambient space is bounded from below on the set of timelike unit vectors. Moreover, if we ass...

Abstract. Many tests for a changing mean in a time series require the estimation of a long run variance. Recent research of Crainiceanu and Vogelsang (2001) suggests that tests involving a long run variance estimate exhibit non-monotonic power. We propose an estimate of long run variances that allows for a time varying mean. In this way, we are able to avoid non-monotonic power while still reta...

The Harary index is defined as the sum of reciprocals distances between all pairs vertices a connected graph G = (V, E). In this paper we introduce Index Power 3 Tree Mean graphs.