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We propose three test criteria each of which is appropriate for testing, respectively, the equivalence hypotheses of symmetry, of homogeneity, and of independence, with multivariate data. All quantities have the common feature of involving…
Ergodic optimization aims to describe dynamically invariant probability measures that maximize the integral of a given function. For a wide class of intrinsically ergodic subshifts over a finite alphabet, we show that the space of…
This paper proposes a max-test for testing (possibly infinitely) many zero parameter restrictions in an extremum estimation framework. The test statistic is formed by estimating key parameters one at a time based on many empirical loss…
Under certain general conditions, we prove that the stable central limit theorem holds in the total variation distance and get its optimal convergence rate for all $\alpha \in (0,2)$. Our method is by two measure decompositions, one step…
Understanding the asymptotic behavior of physical quantities in the thermodynamic limit is a fundamental problem in statistical mechanics. In this paper, we study how fast the eigenstate expectation values of a local operator converge to a…
We introduce a new entanglement measure based on optimal entanglement witness. First of all, we show that the entanglement measure satisfies some necessary properties, including zero entanglements for all separable states, convexity,…
Consider the stationary measure of open asymmetric simple exclusion process (ASEP) on the lattice $\{1,\dots,n\}$. Taking $n$ to infinity while fixing the jump rates, this measure converges to a measure on the semi-infinite lattice. In the…
The thermodynamic definition of entropy can be extended to nonequilibrium systems based on its relation to information. To apply this definition in practice requires access to the physical system's microstates, which may be prohibitively…
We introduce a class of continuous maps f of a compact metric space I admitting inducing schemes and describe the tower constructions associated with them. We then establish a thermodynamical formalism, i.e., describe a class of real-valued…
We find sufficient conditions for bounded density shifts to have a unique measure of maximal entropy. We also prove that every measure of maximal entropy of a bounded density shift is fully supported. As a consequence of this, we obtain…
Various soft materials share some common features, such as significant entropic effect, large fluctuations, sensitivity to thermodynamic conditions, and mesoscopic characteristic spatial and temporal scales. However, no quantitative…
We consider the problem of estimating the population probability distribution given a finite set of multivariate samples, using the maximum entropy approach. In strict keeping with Jaynes' original definition, our precise formulation of the…
An unconventional approach for optimal stopping under model ambiguity is introduced. Besides ambiguity itself, we take into account how ambiguity-averse an agent is. This inclusion of ambiguity attitude, via an $\alpha$-maxmin nonlinear…
A test of the null hypothesis that a hazard rate is monotone nondecreasing, versus the alternative that it is not, is proposed. Both the test statistic and the means of calibrating it are new. Unlike previous approaches, neither is based on…
In this paper for a class of symmetric multiparty pure states we consider a conjecture related to the geometric measure of entanglement: 'for a symmetric pure state, the closest product state in terms of the fidelity can be chosen as a…
In high-contrast composites, the electric (or stress) field may exhibit significant amplification in the narrow region between inclusions. The behavior of the solution depends on the distance $\epsilon$ between the inclusions, which tends…
Asymptotic optimality is a key theoretical property in model averaging. Due to technical difficulties, existing studies rely on restricted weight sets or the assumption that there is no true model with fixed dimensions in the candidate set.…
We study ergodic-theoretic properties of coded shift spaces. A coded shift space is defined as a closure of all bi-infinite concatenations of words from a fixed countable generating set. We derive sufficient conditions for the uniqueness of…
When constructing models of the world, we aim for optimal compressions: models that include as few details as possible while remaining as accurate as possible. But which details -- or features measured in data -- should we choose to include…
In nonstandard testing environments, researchers often derive ad hoc tests with correct (asymptotic) size, but their optimality properties are typically unknown a priori and difficult to assess. This paper develops a numerical framework for…