Related papers: Simultaneous Confidence Bands for Functional Data …
We consider nonparametric regression in the context of functional data, that is, when a random sample of functions is observed on a fine grid. We obtain a functional asymptotic normality result allowing to build simultaneous confidence…
When collections of functional data are too large to be exhaustively observed, survey sampling techniques provide an effective way to estimate global quantities such as the population mean function. Assuming functional data are collected…
In this paper, we construct the simultaneous confidence band (SCB) for the nonparametric component in partially linear panel data models with fixed effects. We remove the fixed effects, and further obtain the estimators of parametric and…
Inference via simultaneous confidence band is studied for stationary covariance function of dense functional data. A two-stage estimation procedure is proposed based on spline approximation, the first stage involving estimation of all the…
Quantifying uncertainty using confidence regions is a central goal of statistical inference. Despite this, methodologies for confidence bands in Functional Data Analysis are still underdeveloped compared to estimation and hypothesis…
Given a functional central limit (fCLT) for an estimator and a parameter transformation, we construct random processes, called functional delta residuals, which asymptotically have the same covariance structure as the limit process of the…
The Gaussian Kinematic Formula (GKF) is a powerful and computationally efficient tool to perform statistical inference on random fields and became a well-established tool in the analysis of neuroimaging data. Using realistic error models,…
In this paper we develop procedures to construct simultaneous confidence bands for $\tilde p$ potentially infinite-dimensional parameters after model selection for general moment condition models where $\tilde p$ is potentially much larger…
Safety-critical control systems, such as spacecraft performing proximity operations, must provide formal safety guarantees despite stochastic uncertainties from state estimation and unmodeled dynamics. Although Control Barrier Functions…
Functional Time Series are sequences of dependent random elements taking values on some functional space. Most of the research on this domain is focused on producing a predictor able to forecast the value of the next function having…
We consider the problem of joint simultaneous confidence band (JSCB) construction for regression coefficient functions of time series scalar-on-function linear regression when the regression model is estimated by roughness penalization…
When the study variable is functional and storage capacities are limited or transmission costs are high, selecting with survey sampling techniques a small fraction of the observations is an interesting alternative to signal compression…
We propose a new framework for the simultaneous inference of monotone and smoothly time-varying functions under complex temporal dynamics. This will be done utilizing the monotone rearrangement and the nonparametric estimation. We…
Band-limited functions are fundamental objects that are widely used in systems theory and signal processing. In this paper we refine a recent nonparametric, nonasymptotic method for constructing simultaneous confidence regions for…
When the underlying random variables are Gaussian, the classical Central Limit Theorem (CLT) is trivial, but the functional CLT is not. The objective of the paper is to investigate the functional CLT for stationary Gaussian processes in the…
Simultaneous confidence bands (SCBs) for percentiles in linear regression are valuable tools with many applications. In this paper, we propose a novel criterion for comparing SCBs for percentiles, termed the Minimum Area Confidence Set…
We consider stochastic approximations of sampling algorithms, such as Stochastic Gradient Langevin Dynamics (SGLD) and the Random Batch Method (RBM) for Interacting Particle Dynamcs (IPD). We observe that the noise introduced by the…
Control Barrier Functions (CBFs) aim to ensure safety by constraining the control input at each time step so that the system state remains within a desired safe region. This paper presents a framework for CBFs in stochastic systems in the…
The Gaussian Kinematic Formula (GKF, see Adler and Taylor (2007,2011)) is an extremely powerful tool allowing for explicit analytic predictions of expected values of Minkowski functionals under realistic experimental conditions for…
We provide a generalization of the Gaussian Kinematic Formula (GKF) in Taylor(2006) for multivariate, heterogeneous Gaussian-related fields. The fields under consideration are non-Gaussian fields built out of smooth, independent Gaussian…