Results 61 to 70 of about 36,851 (159)
Characterization of metric spaces whose free space is isometric to $\ell_1$
, 2015 We characterize metric spaces whose Lipschitz free space is isometric to $\ell_1$. In particular, the Lipschitz free space over an ultrametric space is not isometric to $\ell_1(\Gamma)$ for any set $\Gamma$.
Dalet, Aude +2 more
core
Some Remarks on Schauder Bases in Lipschitz Free Spaces [PDF]
Bulletin of the Belgian Mathematical Society - Simon Stevin, 2020 We show that the basis constant of every retractional Schauder basis on the Free space of a graph circle increases with the radius. As a consequence, there exists a uniformly discrete subset $M\subset\mathbb{R}^2$ such that $\mathcal F(M)$ does not have a retractional Schauder basis. Furthermore, we show that for any net $ N\subseteq\mathbb{R}^n$ there
openaire +3 more sources
Adaptive Estimation for Weakly Dependent Functional Times Series
Journal of Time Series Analysis, EarlyView.ABSTRACT We propose adaptive mean and autocovariance function estimators for stationary functional time series under 𝕃p−m‐approximability assumptions. These estimators are designed to adapt to the regularity of the curves and to accommodate both sparse and dense data designs.
Hassan Maissoro +2 more
wiley +1 more source
Approximation and Schur properties for Lipschitz free spaces over compact metric spaces
, 2015 We prove that for any separable Banach space $X$, there exists a compact metric space which is homeomorphic to the Cantor space and whose Lipschitz-free space contains a complemented subspace isomorphic to $X$.
Hájek, Petr +2 more
core
A Note on Local Polynomial Regression for Time Series in Banach Spaces
Journal of Time Series Analysis, EarlyView.ABSTRACT This work extends local polynomial regression to Banach space‐valued time series for estimating smoothly varying means and their derivatives in non‐stationary data. The asymptotic properties of both the standard and bias‐reduced Jackknife estimators are analyzed under mild moment conditions, establishing their convergence rates.
Florian Heinrichs
wiley +1 more source
Sequential Outlier Detection in Nonstationary Time Series
Journal of Time Series Analysis, EarlyView.ABSTRACT A novel method for sequential outlier detection in nonstationary time series is proposed. The method tests the null hypothesis of “no outlier” at each time point, addressing the multiple testing problem by bounding the error probability of successive tests, using extreme‐value theory. The asymptotic properties of the test statistic are studied
Florian Heinrichs +2 more
wiley +1 more source
Products of Lipschitz-free spaces and applications [PDF]
Studia Mathematica, 2015 We show that, given a Banach space $X$, the Lipschitz-free space over $X$, denoted by $\mathcal{F}(X)$, is isomorphic to $(\sum_{n=1}^\infty \mathcal{F}(X))_{\ell_1}$. Some applications are presented, including a non-linear version of Pelczy ki's decomposition method for Lipschitz-free spaces and the identification up to isomorphism between $\mathcal ...
openaire +3 more sources
Empirical‐Process Limit Theory and Filter Approximation Bounds for Score‐Driven Time Series Models
Journal of Time Series Analysis, EarlyView.ABSTRACT This article examines the filtering and approximation‐theoretic properties of score‐driven time series models. Under specific Lipschitz‐type and tail conditions, new results are derived, leading to maximal and deviation inequalities for the filtering approximation error using empirical process theory.
Enzo D'Innocenzo
wiley +1 more source
Lipschitz-Free Spaces over Cantor Sets and Approximation Properties
Mediterranean Journal of Mathematics, 2023 AbstractLet $$K=2^\mathbb {N}$$ K = 2 N be the Cantor set, let $$\mathcal {M}$$ M be the set of all metrics d on K that give its usual ...
openaire +3 more sources
Testing Distributional Granger Causality With Entropic Optimal Transport
Journal of Time Series Analysis, EarlyView.ABSTRACT We develop a novel nonparametric test for Granger causality in distribution based on entropic optimal transport. Unlike classical mean‐based approaches, the proposed method directly compares the full conditional distributions of a response variable with and without the history of a candidate predictor.
Tao Wang
wiley +1 more source