Non-Asymptotic Confidence Sets for Circular Means

Non-Asymptotic Confidence Sets for Circular Means

The mean of data on the unit circle is defined as the minimizer of the average squared Euclidean distance to the data. Based on Hoeffding’s mass concentration inequalities, non-asymptotic confidence sets for circular means are constructed which are universal in the sense that they require no distributional assumptions. These are then compared with asymptotic confidence sets in simulations and f...

Global Non-asymptotic Confidence Sets for General Linear Models

In this paper we consider the problem of constructing confidence sets for the parameters of general linear models. Based on subsampling techniques and building on earlier exact finite sample results due to Hartigan, we compute the exact probability that the true parameters belong to certain regions in the parameter space. By intersecting these regions, a confidence set containing the true param...

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 ...

Adaptive non-asymptotic confidence balls in density estimation

Confidence Sets for Network Structure

Latent variable models are frequently used to identify structure in dichotomous network data, in part because they give rise to a Bernoulli product likelihood that is both well understood and consistent with the notion of exchangeable random graphs. In this article we propose conservative confidence sets that hold with respect to these underlying Bernoulli parameters as a function of any given ...