Related papers: Effective and flexible depth-based inference for f…

Measurement error is an important problem that has not been very well studied in the context of Functional Data Analysis. To the best of our knowledge, there are no existing methods that address the presence of functional measurement errors…

Robust estimation of location is a fundamental problem in statistics, particularly in scenarios where data contamination by outliers or model misspecification is a concern. In univariate settings, methods such as the sample median and…

In this paper, we propose a new statistical inference method for massive data sets, which is very simple and efficient by combining divide-and-conquer method and empirical likelihood. Compared with two popular methods (the bag of little…

We consider marked empirical processes indexed by a randomly projected functional covariate to construct goodness-of-fit tests for the functional linear model with scalar response. The test statistics are built from continuous functionals…

A fast nonparametric procedure for classifying functional data is introduced. It consists of a two-step transformation of the original data plus a classifier operating on a low-dimensional hypercube. The functional data are first mapped…

The goal of this paper is to provide some tools for nonparametric estimation and inference in psychological and economic experiments. We consider an experimental framework in which each of $n$subjects provides $T$ responses to a vector of…

Considering the case where the response variable is a categorical variable and the predictor is a random function, two novel functional sufficient dimensional reduction (FSDR) methods are proposed based on mutual information and square loss…

It is often of interest to make inference on an unknown function that is a local parameter of the data-generating mechanism, such as a density or regression function. Such estimands can typically only be estimated at a…

We consider functional linear regression models where functional outcomes are associated with scalar predictors by coefficient functions with shape constraints, such as monotonicity and convexity, that apply to sub-domains of interest. To…

An inference procedure is proposed to provide consistent estimators of parameters in a modal regression model with a covariate prone to measurement error. A score-based diagnostic tool exploiting parametric bootstrap is developed to assess…

The Wasserstein distance is an attractive tool for data analysis but statistical inference is hindered by the lack of distributional limits. To overcome this obstacle, for probability measures supported on finitely many points, we derive…

The estimation of cumulative distribution functions (CDF) is an important learning task with a great variety of downstream applications, such as risk assessments in predictions and decision making. In this paper, we study functional…

Understanding what information neural networks capture is an essential problem in deep learning, and studying whether different models capture similar features is an initial step to achieve this goal. Previous works sought to define metrics…

Tests for structural breaks in time series should ideally be sensitive to breaks in the parameter of interest, while being robust to nuisance changes. Statistical analysis thus needs to allow for some form of nonstationarity under the null…

In Functional Data Analysis, data are commonly assumed to be smooth functions on a fixed interval of the real line. In this work, we introduce a comprehensive framework for the analysis of functional data, whose domain is a two-dimensional…

Although there is an extensive literature on the eigenvalues of high-dimensional sample covariance matrices, much of it is specialized to independent components (IC) models -- in which observations are represented as linear transformations…

While widely used as a general method for uncertainty quantification, the bootstrap method encounters difficulties that raise concerns about its validity in practical applications. This paper introduces a new resampling-based method, termed…

Measuring a strength of dependence of random variables is an important problem in statistical practice. In this paper, we propose a new function valued measure of dependence of two random variables. It allows one to study and visualize…

We introduce a bootstrap procedure for high-frequency statistics of Brownian semistationary processes. More specifically, we focus on a hypothesis test on the roughness of sample paths of Brownian semistationary processes, which uses an…

We propose a new notion called `extremal depth' (ED) for functional data, discuss its properties, and compare its performance with existing concepts. The proposed notion is based on a measure of extreme `outlyingness'. ED has several…