Results 121 to 130 of about 417,873 (284)

Reformulations of Quadratic Programs for Lipschitz Continuity

IEEE Control Systems Letters
Submitted to IEEE Control Systems Letters (L-CSS)
Devansh R. Agrawal, Haejoon Lee, Dimitra Panagou   +2 more
openaire   +4 more sources

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

Robust Estimation and Inference for Time‐Varying Unconditional Volatility

Journal of Time Series Analysis, EarlyView.
ABSTRACT We derive a general and robust estimator of a large class of parametric specifications of time‐varying unconditional volatility of financial returns, both univariate and multivariate, and establish the Consistency and Asymptotic Normality (CAN) of the estimator.
Adam Lee, Rickard Sandberg, Genaro Sucarrat   +2 more
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, Patrick Bastian, Holger Dette   +2 more
wiley   +1 more source

Lipschitz functions of continuous functions [PDF]

Pacific Journal of Mathematics, 1953
Marx, Imanuel, Piranian, George
openaire   +3 more sources

On Schwarz-Pick type inequality and Lipschitz continuity for solutions to nonhomogeneous biharmonic equations

, 2023
The purpose of this paper is to study the Schwarz-Pick type inequality and the Lipschitz continuity for the solutions to the nonhomogeneous biharmonic equation: $\Delta(\Delta f)=g$, where $g:$ $\overline{\ID}\rightarrow\mathbb{C}$ is a continuous ...
Li, Peijin, Ponnusamy, Saminathan, Luo, Qinghong, Li, Yaxiang   +3 more
core  

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

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

Principles of Lipschitz continuity in neural networks

CoRR
Deep learning has achieved remarkable success across a wide range of domains, significantly expanding the frontiers of what is achievable in artificial intelligence. Yet, despite these advances, critical challenges remain -- most notably, ensuring robustness to small input perturbations and generalization to out-of-distribution data.
openaire   +2 more sources

Approximation Theory for Lipschitz Continuous Transformers

CoRR
Stability and robustness are critical for deploying Transformers in safety-sensitive settings. A principled way to enforce such behavior is to constrain the model's Lipschitz constant. However, approximation-theoretic guarantees for architectures that explicitly preserve Lipschitz continuity have yet to be established.
Takashi Furuya, Davide Murari, Carola-Bibiane Schönlieb   +2 more
openaire   +2 more sources