Related papers: Transformed Fr\'echet Means for Robust Estimation …
We establish half-space type results for a class of height-dependent weighted minimal surfaces in $\mathbb{R}^3$, namely critical points of a weighted area functional whose weight depends on the height. When the weight has at most quadratic…
This paper proposes consistent estimators for transformation parameters in semiparametric models. The problem is to find the optimal transformation into the space of models with a predetermined regression structure like additive or…
Several classes of tempered measures are characterised that are eigenmeasures of the Fourier transform, the latter viewed as a linear operator on (generally unbounded) Radon measures on $\RR^d$. In particular, we classify all periodic…
In this paper, we consider parametric transformed Fay-Herriot models, and clarify conditions on transformations under which the estimator of the transformation is consistent. It is shown that the dual power transformation satisfies the…
We study a generalization of the Fr\'echet mean on metric spaces, which we call $\phi$-means. Our generalization is indexed by a convex function $\phi$. We find necessary and sufficient conditions for $\phi$-means to be finite and provide a…
A modelling framework suitable for detecting shape shifts in functional profiles combining the notion of Fr\'echet mean and the concept of deformation models is developed and proposed. The generalized mean sense offered by the Fr\'echet…
The convolution quadrature method originally developed for the Riemann-Liouville fractional calculus is extended in this work to the Hadamard fractional calculus by using the exponential type meshes. Local truncation error analysis is…
We study the problem of estimating a mean pattern from a set of similar curves in the setting where the variability in the data is due to random geometric deformations and additive noise. We propose an estimator based on the notion of…
Various results based on some convexity assumptions (involving the exponential map along with affine maps, geodesics and convex hulls) have been recently established on Hadamard manifolds. In this paper we prove that these conditions are…
We investigate corrector estimates for the solutions of a thermoelasticity problem posed in a highly heterogeneous two-phase medium and its corresponding two-scale thermoelasticity model which was derived in an earlier paper by two-scale…
We initiate a systematic study of intrinsic dimensional versions of classical functional inequalities which capture refined properties of the underlying objects. We focus on model spaces: Euclidean space, Hamming cube, and manifolds of…
Variation of empirical Fr\'echet means on a metric space with curvature bounded above is encoded via random fields indexed by unit tangent vectors. A central limit theorem shows these random tangent fields converge to a Gaussian such field…
We investigate an algorithm named histogram transform ensembles (HTE) density estimator whose effectiveness is supported by both solid theoretical analysis and significant experimental performance. On the theoretical side, by decomposing…
We consider regression with square loss and general classes of functions without the boundedness assumption. We introduce a notion of offset Rademacher complexity that provides a transparent way to study localization both in expectation and…
A novel algorithm is proposed for quantitative comparisons between compact surfaces embedded in the three-dimensional Euclidian space. The key idea is to identify those objects with the associated surface measures and compute a weak…
Given a frequency $\lambda$, we study general Dirichlet series $\sum a_n e^{-\lambda_n s}$. First, we give a new condition on $\lambda$ which ensures that a somewhere convergent Dirichlet series defining a bounded holomorphic function in…
We develop an approach for estimating models described via conditional moment restrictions, with a prototypical application being non-parametric instrumental variable regression. We introduce a min-max criterion function, under which the…
Barycenters (aka Fr\'echet means) were introduced in statistics in the 1940's and popularized in the fields of shape statistics and, later, in optimal transport and matrix analysis. They provide the most natural extension of linear…
This revisit gives a survey on the analytical methods for the inverse exponential Radon transform which has been investigated in the past three decades from both mathematical interests and medical applications such as nuclear medicine…
A bias-reduced estimator is proposed for the mean absolute deviation parameter of a median regression model. A workaround is devised for the lack of smoothness in the sense conventionally required in general bias-reduced estimation. A local…