Related papers: On consistency and inconsistency of nonparametric …
It is well-known that density estimation on the unit interval is asymptotically equivalent to a Gaussian white noise experiment, provided the densities are sufficiently smooth and uniformly bounded away from zero. We show that a uniform…
We show that the stability problem and the problem of constructing Barabanov norms can be resolved for planar linear switching systems in an explicit form. This can be done for every compact control set of $2 \times 2$ matrices. If the…
This paper studies the problem of testing whether a function is monotone from a nonparametric Bayesian perspective. Two new families of tests are constructed. The first uses constrained smoothing splines, together with a hierarchical…
We present simple conditions for Bayesian consistency in the supremum metric. The key to the technique is a triangle inequality which allows us to explicitly use weak convergence, a consequence of the standard Kullback--Leibler support…
The role of consistent measures in the rigorous construction of nonabelian lattice theories is analized. General conditions that measures must fulfill to insure consistency, positivity and a mass gap are obtained. The impact of nongeneric…
Motivated by set estimation problems, we consider three closely related shape conditions for compact sets: positive reach, r-convexity and rolling condition. First, the relations between these shape conditions are analyzed. Second, we…
Bound-to-Bound Data Collaboration (B2BDC) provides a natural framework for addressing both forward and inverse uncertainty quantification problems. In this approach, QOI (quantity of interest) models are constrained by related experimental…
In modern data analysis, nonparametric measures of discrepancies between random variables are particularly important. The subject is well-studied in the frequentist literature, while the development in the Bayesian setting is limited where…
The concentration of measure phenomenon in Gauss' space states that every $L$-Lipschitz map $f$ on $\mathbb R^n$ satisfies \[ \gamma_{n} \left(\{ x : | f(x) - M_{f} | \geqslant t \} \right) \leqslant 2 e^{ - \frac{t^2}{ 2L^2} }, \quad t>0,…
We consider the goodness of fit testing problem for linear stochastic differential equation (Ornstein-Uhlenbeck process). The basic hypothesis is supposed to be composite with two-dimensional unknown parameter. We study two goodness of fit…
We use martingales to study Bayesian consistency. We derive sufficient conditions for both Hellinger and Kullback-Leibler consistency, which do not rely on the use of a sieve. Alternative sufficient conditions for Hellinger consistency are…
In a smooth semiparametric estimation problem, the marginal posterior for the parameter of interest is expected to be asymptotically normal and satisfy frequentist criteria of optimality if the model is endowed with a suitable prior. It is…
A distributed binary hypothesis testing problem is studied with one observer and two decision centers. Achievable type-II error exponents are derived for testing against conditional independence when the observer communicates with the two…
A central problem in signal processing and communications is to design signals that are compact both in time and frequency. Heisenberg's uncertainty principle states that a given function cannot be arbitrarily compact both in time and…
We consider abstract nonlinear equations of the form $A u = \lambda u + I'(u)$, where $A$ is a self-adjoint operator with compact resolvent on a Hilbert space $H$, $\lambda \in \mathbb{R}$ is a parameter, and $u \mapsto I'(u)$ is a…
The paper introduces robust independence tests with non-asymptotically guaranteed significance levels for stochastic linear time-invariant systems, assuming that the observed outputs are synchronous, which means that the systems are driven…
We derive the Euler-Lagrange equations for minimizers of causal variational principles in the non-compact setting with constraints, possibly prescribing symmetries. Considering first variations, we show that the minimizing measure is…
This paper concerns the approximation of probability measures on $\mathbf{R}^d$ with respect to the Kullback-Leibler divergence. Given an admissible target measure, we show the existence of the best approximation, with respect to this…
A panel dataset satisfies marginal homogeneity if the time-specific marginal distributions are homogeneous or time-invariant. Marginal homogeneity is relevant in many economic settings, including dynamic discrete games,…
We introduce a new perspective on the classical Nirenberg problem of understanding the possible Gauss curvatures of metrics on $S^{2}$ conformal to the round metric. A key tool is to employ the smooth Cheeger-Gromov compactness theorem to…