Confidence Regions in Linear Functional Relationships

Approximate Confidence Regions for Minimax-Linear Estimators

Minimax estimation is based on the idea that the quadratic risk func tion for the estimate is not minimized over the entire parameter space IR but only over an area B that is restricted by a priori knowledge If all restrictions de ne a convex area this area can often be enclosed in an ellipsoid of the form B f T rg The ellipsoid has a larger volume than the cuboid Hence the transition to an e...

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...

Rayleigh Confidence Regions based on Record Data

This paper presents exact joint confidence regions for the parameters of the Rayleigh distribution based on record data. By providing some appropriate pivotal quantities, we construct several joint confidence regions for the Rayleigh parameters. These joint confidence regions are useful for constructing confidence regions for functions of the unknown parameters. Applications of the joint confid...

Estimation Of Multiple Linear Functional Relationships

Confidence Regions for Barcodes

The results of [3] suggest a way to sort which barcode intervals correctly belong to the underlying manifold, M , and which can be regarded as topological noise. In particular, when barcodes are computed using sublevel sets of their distance function (see eq 12), all of the barcodes that start later than a linear function of W2(F̂n, F ) can be assumed to correctly reflect the betti numbers of M ...