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We introduce a novel function-on-function linear quantile regression model to characterize the entire conditional distribution of a functional response for a given functional predictor. Tensor cubic $B$-splines expansion is used to…

This paper studies linear reconstruction of partially observed functional data which are recorded on a discrete grid. We propose a novel estimation approach based on approximate factor models with increasing rank taking into account…

In functional linear regression, the slope ``parameter'' is a function. Therefore, in a nonparametric context, it is determined by an infinite number of unknowns. Its estimation involves solving an ill-posed problem and has points of…

Incremental learning often encounter challenges such as overfitting to new data and catastrophic forgetting of old data. Existing methods can effectively extend the model for new tasks while freezing the parameters of the old model, but…

Regression discontinuity designs have become one of the most popular research designs in empirical economics. We argue, however, that widely used approaches to building confidence intervals in regression discontinuity designs exhibit…

We develop theory leading to testing procedures for the presence of a change point in the intraday volatility pattern. The new theory is developed in the framework of Functional Data Analysis. It is based on a model akin to the stochastic…

Frailty models are often the model of choice for heterogeneous survival data. A frailty model contains both random effects and fixed effects, with the random effects accommodating for the correlation in the data. Different estimation…

In demographic literature, forecast uncertainty is often quantified with a statistical model. This model-based approach may potentially suffer from drawbacks, namely model misspecification, selection effect, and lack of finite-sample…

A goodness-of-fit test for the Functional Linear Model with Scalar Response (FLMSR) with responses Missing at Random (MAR) is proposed in this paper. The test statistic relies on a marked empirical process indexed by the projected…

Rolling bearings are subject to various faults due to its long-time operation under harsh environment, which will lead to unexpected breakdown of machinery system and cause severe accidents. Deep learning methods recently have gained…

When dynamical systems that produce rhythmic behaviors operate within hard limits, they may exhibit limit cycles with sliding components, that is, closed isolated periodic orbits that make and break contact with a constraint surface.…

Functional data analysis tools, such as function-on-function regression models, have received considerable attention in various scientific fields because of their observed high-dimensional and complex data structures. Several statistical…

We address the challenge of estimation in the context of constant linear effect models with dense functional responses. In this framework, the conditional expectation of the response curve is represented by a linear combination of…

Repetitive motion tasks are common in robotics, but performance can degrade over time due to environmental changes and robot wear and tear. Iterative learning control (ILC) improves performance by using information from previous iterations…

In this paper, we focus on the problem of conformal prediction with conditional guarantees. Prior work has shown that it is impossible to construct nontrivial prediction sets with full conditional coverage guarantees. A wealth of research…

Scaling laws have emerged as a unifying lens for understanding and guiding the training of large language models (LLMs). However, existing studies predominantly focus on the final-step loss, leaving open whether the entire loss dynamics…

Safety-critical infrastructures must operate in a safe and reliable way. Fault tree analysis is a widespread method used for risk assessment of these systems: fault trees (FTs) are required by, e.g., the Federal Aviation Administration and…

In this paper we shall review the common problems associated with Piecewise Linear Separation incremental algorithms. This kind of neural models yield poor performances when dealing with some classification problems, due to the evolving…

Using first principles from inference, we design a set of functionals for the purposes of \textit{ranking} joint probability distributions with respect to their correlations. Starting with a general functional, we impose its desired…

This paper focuses on the analysis of spatially correlated functional data. The between-curve correlation is modeled by correlating functional principal component scores of the functional data. We propose a Spatial Principal Analysis by…