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Data depth is a well-known and useful nonparametric tool for analyzing functional data. It provides a novel way of ranking a sample of curves from the center outwards and defining robust statistics, such as the median or trimmed means. It…
Interval analysis, when applied to the so called problem of experimental data fitting, appears to be still in its infancy. Sometimes, partly because of the unrivaled reliability of interval methods, we do not obtain any results at all.…
Starting from a linear fractional representation of a linear system affected by constant parametric uncertainties, we demonstrate how to enhance standard robust analysis tests by taking available (noisy) input-output data of the uncertain…
The paper concerns inference in the ill-conditioned functional response model, which is a part of functional data analysis. In this regression model, the functional response is modeled using several independent scalar variables. To verify…
The focus of this book is on the analysis of regularization methods for solving \emph{nonlinear inverse problems}. Specifically, we place a strong emphasis on techniques that incorporate supervised or unsupervised data derived from prior…
Uncertainties in a structure is inevitable, which generally lead to variation in dynamic response predictions. For a complex structure, brute force Monte Carlo simulation for response variation analysis is infeasible since one single run…
This paper is devoted to developing and applications of a generalized differential theory of variational analysis that allows us to work in incomplete normed spaces, without employing conventional variational techniques based on…
It is not unusual for a data analyst to encounter data sets distributed across several computers. This can happen for reasons such as privacy concerns, efficiency of likelihood evaluations, or just the sheer size of the whole data set. This…
Differential analysis is a routine procedure in the statistical analysis toolbox across many applied fields, including quantitative proteomics, the main illustration of the present paper. The state-of-the-art limma approach uses a…
The concept of generalized functions taking values in a differentiable manifold is extended to a functorial theory. We establish several characterization results which allow a global intrinsic formulation both of the theory of…
A fundamental problem in the practice and teaching of data science is how to evaluate the quality of a given data analysis, which is different than the evaluation of the science or question underlying the data analysis. Previously, we…
High-frequency financial data can be collected as a sequence of curves over time; for example, as intra-day price, currently one of the topics of greatest interest in finance. The Functional Data Analysis framework provides a suitable tool…
With the advance of modern technology, more and more data are being recorded continuously during a time interval or intermittently at several discrete time points. They are both examples of "functional data", which have become a prevailing…
Missing values often limit the usage of data analysis or cause falsification of results. Therefore, methods of missing value imputation (MVI) are of great significance. However, in general, there is no universal, fair MVI method for…
We study factor models that combine latent factors with firm characteristics and propose a new framework for modeling, estimating, and inferring pricing errors. Following Zhang (2024), our approach decomposes mispricing into two distinct…
This article presents a reformulation of the Theory of Functional Connections: a general methodology for functional interpolation that can embed a set of user-specified linear constraints. The reformulation presented in this paper exploits…
It is common to hold prior beliefs that are not characterized by points in the parameter space but instead are relational in nature and can be described by a linear subspace. While some previous work has been done to account for such prior…
Sensitivity analysis is popular in dealing with missing data problems particularly for non-ignorable missingness. It analyses how sensitively the conclusions may depend on assumptions about missing data e.g. missing data mechanism (MDM). We…
Happ and Greven (2018) developed a methodology for principal components analysis of multivariate functional data observed on different dimensional domains. Their approach relies on an estimation of univariate functional principal components…
We introduce a framework for automatically choosing data structures to support efficient computation of analytical workloads. Our contributions are twofold. First, we introduce a novel low-level intermediate language that can express the…