Asymptotic confidence regions for density ridges

Non-Asymptotic Confidence Regions for the Least-Squares Estimate

We propose a new finite sample system identification method, called Sign-Perturbed Sums (SPS), to estimate the parameters of dynamical systems under mild statistical assumptions. The proposed method constructs non-asymptotic confidence regions that include the leastsquares (LS) estimate and are guaranteed to contain the true parameters with a user-chosen exact probability. Our method builds on ...

Joint Confidence Regions

Confidence intervals are one of the most important topics in mathematical statistics which are related to statistical hypothesis tests. In a confidence interval, the aim is that to find a random interval that coverage the unknown parameter with high probability. Confidence intervals and its different forms have been extensively discussed in standard statistical books. Since the most of stati...

Asymptotic Behavior of Confidence Regions in the Change-Point Problem

The confidence estimation of the change-point is considered. The asymptotic behavior of the coverage probability and the expected width of a traditional confidence region is derived as the threshold constant increases. The nature of this bound is related to information numbers and first passage probabilities for random walks. In the situation when preand after-change distributions belong to one...

Asymptotic global confidence regions in parametric shape estimation problems

We introduce confidence region techniques for analyzing and visualizing the performance of two-dimensional parametric shape estimators. Assuming an asymptotically normal and efficient estimator for a finite parameterization of the object boundary, Cramér-Rao bounds are used to define an asymptotic confidence region, centered around the true boundary. Computation of the probability that an entir...

Adaptive non-asymptotic confidence balls in density estimation