1,236 research outputs found
Bi-log-concave distribution functions
Nonparametric statistics for distribution functions F or densities f=F' under
qualitative shape constraints provides an interesting alternative to classical
parametric or entirely nonparametric approaches. We contribute to this area by
considering a new shape constraint: F is said to be bi-log-concave, if both
log(F) and log(1 - F) are concave. Many commonly considered distributions are
compatible with this constraint. For instance, any c.d.f. F with log-concave
density f = F' is bi-log-concave. But in contrast to the latter constraint,
bi-log-concavity allows for multimodal densities. We provide various
characterizations. It is shown that combining any nonparametric confidence band
for F with the new shape-constraint leads to substantial improvements,
particularly in the tails. To pinpoint this, we show that these confidence
bands imply non-trivial confidence bounds for arbitrary moments and the moment
generating function of F
Aubry sets vs Mather sets in two degrees of freedom
We study autonomous Tonelli Lagrangians on closed surfaces. We aim to clarify
the relationship between the Aubry set and the Mather set, when the latter
consists of periodic orbits which are not fixed points. Our main result says
that in that case the Aubry set and the Mather set almost always coincide.Comment: Revised and expanded version. New proof of Lemma 2.3 (formerly Lemma
14
Preliminary development of real time PCR for quantification of Erwinia species infecting potato tubers.
peer reviewe
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