Related papers: Statistical analysis of measures of non-convexity
A new nonparametric estimator of a convex regression function in any dimension is proposed and its convergence properties are studied. We start by using any estimator of the regression function and we \emph{convexify} it by taking the…
In the context of nonparametric regression, we study conditions under which the consistency (and rates of convergence) of estimators built from discretely sampled curves can be derived from the consistency of estimators based on the…
We consider deconvolution from repeated observations with unknown error distribution. So far, this model has mostly been studied under the additional assumption that the errors are symmetric. We construct an estimator for the non-symmetric…
To evaluate disentangled representations several metrics have been proposed. However, theoretical guarantees for conventional metrics of disentanglement are missing. Moreover, conventional metrics do not have a consistent correlation with…
We consider high-dimensional estimation problems where the number of parameters diverges with the sample size. General conditions are established for consistency, uniqueness, and asymptotic normality in both unpenalized and penalized…
This study explores information measures based on extropy, introducing dynamic relative extropy measures for residual and past lifetimes, and investigating their various properties. Furthermore, the study analyzes the relationships between…
Gibbs measures are the main object of study in equilibrium statistical mechanics, and are used in many other contexts, including dynamical systems and ergodic theory, and spatial statistics. However, in a large number of natural instances…
M-estimation, aka empirical risk minimization, is at the heart of statistics and machine learning: Classification, regression, location estimation, etc. Asymptotic theory is well understood when the loss satisfies some smoothness…
The number of times that we can access a system to extract information via quantum metrology is always finite, and possibly small, and realistic amounts of prior knowledge tend to be moderate. Thus theoretical consistency demands a…
Skewness measures can be used to measure the level of asymmetry of a distribution. Given the prevalence of statistical methods that assume underlying symmetry, and also the desire for symmetry in order to make meaningful judgements for…
This paper proposes several tests of restricted specification in nonparametric instrumental regression. Based on series estimators, test statistics are established that allow for tests of the general model against a parametric or…
\textit{Non-statistical dynamics} are those for which a set of points with positive measure (w.r.t. a reference probability measure which is in most examples the Lebesgue on a manifold) do not have a convergent sequence of empirical…
Exploiting the geometric nature of statistical divergences, we devise a way to define associated induced uncertainty measures for discrete and finite probability distributions. We also report new uncertainty measures and discuss their…
In this paper we discuss various connections between geometric discrepancy measures, such as discrepancy with respect to convex sets (and convex sets with smooth boundary in particular), and applications to numerical analysis and…
We consider nonparametric estimation of a regression curve when the data are observed with multiplicative distortion which depends on an observed confounding variable. We suggest several estimators, ranging from a relatively simple one that…
We review the alternative proposals introduced recently in the literature to update the standard formula to estimate the uncertainty on the mean of repeated measurements, and we compare their performances on synthetic examples with normal…
Spaces of quasi-invariant measures supplied with different topologies are studied. Their embeddings, projective decompositions, conditions for their metrizability are investigated. Theorems about convergence of nets of quasi-invariant…
In many statistical studies, the measure of uncertainties like entropy, extropy, varentropy and varextropy of a distribution function is of prime interest. This paper proposes estimators of extropy and varextropy. Proposed estimators are…
Thermodynamically consistent measurements can either preserve statistics (unbiased) or preserve marginal states (non-invasive) but not both. Here we show the existence of metrological tasks which unequally favor each of the aforementioned…
Methods for measuring convexity defects of compacts in R^n abound. However, none of the those measures seems to take into account continuity. Continuity in convexity measure is essential for optimization, stability analysis, global…