10,182 research outputs found
A change-point problem and inference for segment signals
We address the problem of detection and estimation of one or two
change-points in the mean of a series of random variables. We use the formalism
of set estimation in regression: To each point of a design is attached a binary
label that indicates whether that point belongs to an unknown segment and this
label is contaminated with noise. The endpoints of the unknown segment are the
change-points. We study the minimal size of the segment which allows
statistical detection in different scenarios, including when the endpoints are
separated from the boundary of the domain of the design, or when they are
separated from one another. We compare this minimal size with the minimax rates
of convergence for estimation of the segment under the same scenarios. The aim
of this extensive study of a simple yet fundamental version of the change-point
problem is twofold: Understanding the impact of the location and the separation
of the change points on detection and estimation and bringing insights about
the estimation and detection of convex bodies in higher dimensions.Comment: arXiv admin note: substantial text overlap with arXiv:1404.622
Convex set detection
We address the problem of one dimensional segment detection and estimation,
in a regression setup. At each point of a fixed or random design, one observes
whether that point belongs to the unknown segment or not, up to some additional
noise. We try to understand what the minimal size of the segment is so it can
be accurately seen by some statistical procedure, and how this minimal size
depends on some a priori knowledge about the location of the unknown segment
Notes and comments on the ex-post evaluation of the fisheries agreement EU-Morocco
This report presents a summary of the content of the ex-post evaluation of the fishing agreement between the EU and Morocco
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