Related papers: Effective and flexible depth-based inference for f…
The functional delta-method provides a convenient tool for deriving bootstrap consistency of a sequence of plug-in estimators w.r.t. a given functional from bootstrap consistency of the underlying sequence of estimators. It has recently…
A formulation of the density functional theory is constructed on the foundations of entropic inference. The theory is introduced as an application of maximum entropy for inhomogeneous fluids in thermal equilibrium. It is shown that entropic…
We propose a novel method to detect and date structural breaks in the entire distribution of functional data. Theoretical guarantees are developed for our procedure under fewer assumptions than in the existing work. In particular, we…
An algorithm is described that enables efficient deterministic approximate computation of the bootstrap distribution for any linear bootstrap method $T_n^*$, alleviating the need for repeated resampling from observations (resp.…
The problem of comparing the entire second order structure of two functional processes is considered and a $L^2$-type statistic for testing equality of the corresponding spectral density operators is investigated. The test statistic…
Functional data analysis has been a growing field of study in recent decades, and one fundamental task in functional data analysis is estimating the sample location. A notion called statistical depth has been extended from multivariate data…
We investigate asymptotic inference in a linear regression model where both response and regressors are functions, using an estimator based on functional principal components analysis. Although this approach is widely used in functional…
In the context of multivariate functional data with individual phase variation, we develop a robust depth-based approach to estimate the main pattern function when cross-component time warping is also present. In particular, we consider the…
Inference for functional linear models in the presence of heteroscedastic errors has received insufficient attention given its practical importance; in fact, even a central limit theorem has not been studied in this case. At issue,…
Recently, Tibshirani et al. (2016) proposed a method for making inferences about parameters defined by model selection, in a typical regression setting with normally distributed errors. Here, we study the large sample properties of this…
Most existing methods for testing equality of means of functional data from multiple populations rely on assumptions of equal covariance and/or Gaussianity. In this work we provide a new testing method based on a statistic that is…
Statistical analysis of functional data is challenging due to their complex patterns, for which functional depth provides an effective means of reflecting their ordering structure. In this work, we investigate practical aspects of the…
Among inferential problems in functional data analysis, domain selection is one of the practical interests aiming to identify sub-interval(s) of the domain where desired functional features are displayed. Motivated by applications in…
In recent years, bootstrap methods have drawn attention for their ability to approximate the laws of "max statistics" in high-dimensional problems. A leading example of such a statistic is the coordinate-wise maximum of a sample average of…
Hypothesis testing for the slope function in functional linear regression is of both practical and theoretical interest. We develop a novel test for the nullity of the slope function, where testing the slope function is transformed into…
This paper studies an asymptotic framework for conducting inference on parameters of the form $\phi(\theta_0)$, where $\phi$ is a known directionally differentiable function and $\theta_0$ is estimated by $\hat \theta_n$. In these settings,…
Difference-in-differences (DiD) is a cornerstone of causal inference, yet extending it to functional outcomes is not a routine scalar generalization; rather, it entails three fundamental challenges in identification, inference, and…
The functional delta-method has a wide range of applications in statistics. Applications on functionals of empirical processes yield various limit results for classical statistics. To improve the finite sample properties of statistical…
One of the classic concerns in statistics is determining if two samples come from thesame population, i.e. homogeneity testing. In this paper, we propose a homogeneitytest in the context of Functional Data Analysis, adopting an idea from…
In this article, we study whether the slope functions of two scalar-on-function regression models in two samples are associated with any arbitrary transformation along the vertical axis. The problem is formally stated as a statistical…