Functional Regression Research Articles

Exploring Peak Concentric Force and Zero Velocity Synchronization in the Drop Jump.

The application of force is a key aspect of performance during athletic activities. In jumping, the timing and magnitude of force application are important performance factors. The relative timing of forces has only been investigated in the countermovement jump. This study aimed to explore if the synchronization of peak concentric force with the instance of zero velocity during a drop jump impacted performance and examine the relationship of force-time curve shape to performance. Sixty-six state-level athletes (24 males and 42 females) completed drop jumps from a 30 cm box onto dual force plates. The jump with the highest reactive strength index (RSI) score was taken for analysis and classified as synchronous or asynchronous based on the relative timing of peak concentric force and zero velocity. RSI and other force-time variables were compared between groups, and functional principal component analysis (fPCA) was performed on the force-time curves, which were used to perform functional principal component regression (fPCR). Synchronous jumpers exhibited greater RSI scores and shorter contact times compared to asynchronous jumpers. Performance differences were largely driven by improved concentric kinetics, which the fPCR model revealed to have the greatest influence on RSI. Sex was also found to be a significant factor for RSI in the fPCR model. fPCA revealed that greater force application preceding and throughout the amortization phase was positively associated with RSI. The timing of peak concentric force and the shape of the force-time curve are key factors for drop jump performance, and these concepts should be investigated further in other athletic activities.

Asymptotic normality of kernel functional regression estimator based upon twice censored data

Asymptotic normality of kernel functional regression estimator based upon twice censored data

Coefficient Shape Alignment in Multiple Functional Regression

In multivariate functional data analysis, different functional covariates often exhibit homogeneity. The covariates with pronounced homogeneity can be analyzed jointly within the same group, offering a parsimonious approach to modeling multivariate functional data. In this paper, a novel grouped multiple functional regression model with a new regularization approach termed “coefficient shape alignment” is developed to tackle functional covariates homogeneity. The modeling procedure includes two steps: first aggregate covariates into disjoint groups using the new regularization approach; then the grouped multiple functional regression model is established based on the detected grouping structure. In this grouped model, the coefficient functions of covariates in the same group share the same shape, invariant to scaling. The new regularization approach works by penalizing differences in the shape of the coefficients. We establish conditions under which the true grouping structure can be accurately identified and derive the asymptotic properties of the model estimates. Extensive simulation studies are conducted to assess the finite-sample performance of the proposed methods. The practical applicability of the model is demonstrated through real data analysis in the context of sugar quality evaluation. This work offers a novel framework for analyzing the homogeneity of functional covariates and constructing parsimonious models for multivariate functional data.

Heterogeneous functional regression for subgroup analysis

With ever increasing number of features of modern datasets, data heterogeneity is gradually becoming the norm rather than the exception. Whereas classical regressions usually assume all the samples follow a common model, it becomes imperative to identify the heterogeneous relationship in different subsamples. In this article, we propose a new approach to model heterogeneous functional regression relations. We target at the association between a response and a predictor, whose relationship can vary across underlying subgroups and is modeled as an unknown functional of an auxiliary predictor. We introduce a procedure which performs simultaneous parameter estimation and subgroup identification through a fusion type group-wise penalization. We establish the statistical guarantees in terms of non-asymptotic convergence of the parameter estimation. We also establish the oracle property and asymptotic normality of the estimators. We carry out intensive simulations, and illustrate with a new dataset from an Alzheimer’s disease study.

Optimal Subsampling for Functional Quasi-Mode Regression with Big Data

We propose investigating optimal subsampling for functional regression with massive datasets based on the mode value, which is referred to as functional quasi-mode regression, to reduce data volume and alleviate computational burden. Using data-adaptive weights derived from regression residuals, the suggested regression offers enhanced robustness against nonnormal errors compared to traditional least squares or maximum likelihood estimation methods. To estimate the model, we employ B-spline basis functions to approximate the functional coefficient and include a penalty term in the objective function for enforcing smoothness in the resulting estimator. We adopt a computationally efficient mode-expectation-maximization algorithm, augmented by a Gaussian kernel, for numerical estimation. Under mild regularity conditions, we derive the asymptotic distributions of both full data and subsample quasi-mode estimators. The optimal subsampling probabilities by minimizing the asymptotic variance-covariance matrix under A- and L-optimality criteria are identified. These optimal probabilities rely on the full data estimate, prompting the development of a two-step algorithm to approximate the optimal subsampling procedure. The resultant algorithm is processing-efficient and can significantly reduce computational time compared to the full data approach. We also establish the asymptotic normality of the quasi-mode estimator obtained through this two-step algorithm. To assess finite sample performance, we conduct Monte Carlo simulations and analyze air quality data, showcasing the effectiveness of the developed estimator. Supplemental materials for this article are available online.

Identifying influential observations in concurrent functional regression with weighted bootstrap

Identifying influential observations in concurrent functional regression with weighted bootstrap

Metal single-atom interaction with graphitic C3N4 surface based on density functional theory calculations and linear regression analysis

This paper discusses the adsorption of metal single-atoms (SAs) on graphitic C3N4 (gCN) multilayered surface models based on density functional theory (DFT) calculations. We systematically searched stable adsorption sites on gCN and showed that the cavity site is preferred for metal SAs. We also discussed the usefulness of several descriptors, such as the distance between the SA and gCN, charge donation (electron transfer), and atomic radius, for evaluating the SA adsorption energy, based on the linear regression method. In addition, the most stable adsorption energy for fifth- and sixth-row metals can be predicted using only the “group” descriptor of the periodic table. The group descriptor is closely related to the atomic radius, and hence the stability of fifth- and sixth-row metals is determined from the fit between the SA radius and the gCN cavity size. The study findings facilitate the development of various metal-dopant techniques for gCN-based applications.

Strong optimality of kernel functional regression in $$L^p$$ norms with partial response variables and applications

Strong optimality of kernel functional regression in $$L^p$$ norms with partial response variables and applications

Underwater radiated noise explained from ship characteristics and operating conditions - Model obtained from the MARS database

Understanding how ship characteristics and operating conditions impact underwater radiated noise (URN) is key to identifying essential avenues for noise reduction and predict associated risks for the marine life. Previous studies have revealed that current models could only explain up to 50% of the observed variability in URN levels. In this study, we used a unique dataset, collected within the Marine Acoustic Research Station (MARS) project (www.projet-mars. ca/en). The dataset is consisting of ~1000 acoustic signatures from vessels in the St. Lawrence shipping lane (eastern Canada), and 174 high-quality signatures from partner vessels following an optimized measurement protocol and considering design parameters, meteorological, and oceanographic data. Applying functional regression, as described by MacGillivray et al. (2022), we quantified the relationship between vessel characteristics, operation conditions and URN. Our findings quantify the direct effect of the speed, size, and draft on URN across a frequency range of 10-500 Hz. Using these relationships, we propose a tailored URN predictive model representative of the St. Lawrence fleet. We then compare its performance to previously published models and asses the gains linked to the active collaboration of ship owners, contributing to the wide range of available operation conditions available in our dataset.

Understanding excess mortality in 2022: The dual impact of COVID-19 and heatwaves on the Italian elderly population

In this study, we employ a comprehensive approach to model the concurrent effects of the COVID-19 epidemic and heatwaves on all-cause excess mortality. Our investigation uncovers distinct peaks in excess mortality, notably among individuals aged 80 years and older, revealing a strong positive correlation with excess temperatures (ET) during the summer of 2022 in Italy. Furthermore, we identify a notable role played by COVID-19 hospitalizations, exhibiting regional disparities, particularly during the winter months. Leveraging functional data regression, we offer robust and coherent insights into the excess mortality trends observed in Italy throughout 2022.

Functional Data Analysis: An Introduction and Recent Developments.

Functional data analysis (FDA) is a statistical framework that allows for the analysis of curves, images, or functions on higher dimensional domains. The goals of FDA, such as descriptive analyses, classification, and regression, are generally the same as for statistical analyses of scalar-valued or multivariate data, but FDA brings additional challenges due to the high- and infinite dimensionality of observations and parameters, respectively. This paper provides an introduction to FDA, including a description of the most common statistical analysis techniques, their respective software implementations, and some recent developments in the field. The paper covers fundamental concepts such as descriptives and outliers, smoothing, amplitude and phase variation, and functional principal component analysis. It also discusses functional regression, statistical inference with functional data, functional classification and clustering, and machine learning approaches for functional data analysis. The methods discussed in this paper are widely applicable in fields such as medicine, biophysics, neuroscience, and chemistry and are increasingly relevant due to the widespread use of technologies that allow for the collection of functional data. Sparse functional data methods are also relevant for longitudinal data analysis. All presented methods are demonstrated using available software in R by analyzing a dataset on human motion and motor control. To facilitate the understanding of the methods, their implementation, and hands-on application, the code for these practical examples is made available through a code and data supplement and on GitHub.

Functional partially linear single index models with measurement error in both functional and real covariates

In this paper, we investigate the functional partially linear single index models with contaminated functional and real covariates when the functional sample grid is dense. To eliminate the influence of measurement error on the estimations of the proposed models, a two-stage estimation procedure is introduced. In the first stage, we utilize a kernel presmoothing regression to denoise the corrupted functional curves. In the second stage, the fitted functional curves are applied to replace the original ones to obtain the predictor of unknown parameter in parametric component with the attenuation correction method and then we derive the predictor of unknown link function in nonparametric part with kernel method. Meanwhile, in order to improve computational efficiency, functional slice inverse regression method is employed to estimate the functional single index parameter. The asymptotic properties are also stated in this process at the situation of independent and identical distribution sample under some mild conditions. A simulation study and real data analysis are further explored to illustrate the good performance of our methodology.

FAStEN: An Efficient Adaptive Method for Feature Selection and Estimation in High-Dimensional Functional Regressions

Functional regression analysis is an established tool for many contemporary scientific applications. Regression problems involving large and complex data sets are ubiquitous, and feature selection is crucial for avoiding overfitting and achieving accurate predictions. We propose a new, flexible and ultra-efficient approach to perform feature selection in a sparse high dimensional function-on-function regression problem, and we show how to extend it to the scalar-on-function framework. Our method, called FAStEN, combines functional data, optimization, and machine learning techniques to perform feature selection and parameter estimation simultaneously. We exploit the properties of Functional Principal Components and the sparsity inherent to the Dual Augmented Lagrangian problem to significantly reduce computational cost, and we introduce an adaptive scheme to improve selection accuracy. In addition, we derive asymptotic oracle properties, which guarantee estimation and selection consistency for the proposed FAStEN estimator. Through an extensive simulation study, we benchmark our approach to the best existing competitors and demonstrate a massive gain in terms of CPU time and selection performance, without sacrificing the quality of the coefficients’ estimation. The theoretical derivations and the simulation study provide a strong motivation for our approach. Finally, we present an application to brain fMRI data from the AOMIC PIOP1 study. Complete FAStEN code is provided at https://github.com/IBM/funGCN. Supplementary materials for this article are available online.

Exploration of Geographical Environmental Factors Influencing Regional Population Mortality Patterns inChina.

The regional population mortality patterns in China exhibit substantial geographical distribution characteristics. This paper aims to explore the impact and mechanisms of geographical environmental factors on regional population mortality patterns. This study first utilized the data from China's Seventh Population Census to obtain mortality patterns for the 31 provincial-level administrative regions. Subsequently, a functional regression method was employed to explore the geographical environmental driving factors of regional mortality patterns. The study provides a detailed explanation of the mechanisms and marginal contributions of key geographical environmental factors at different age groups. (1) The impact of geographical environmental factors on mortality patterns shows distinct phased characteristics. Mortality patterns before the age of 40 years are hardly influenced by geographical environmental factors, with a noticeable impact beginning at ages 40-69 years and reaching the maximum influence after the age of 70 years. (2) In mortality patterns at ages 40-69 years, average altitude have the most substantial impact, followed by extreme low-temperature days and PM2.5 concentration. In mortality patterns at ages 70-94 years, high-temperature days have the greatest influence, followed by the impact of SO2 concentration. (3) In comparisons based on gender, socioeconomic factors, and geographical environmental factors, gender and urban-rural differences have the most significant impact on regional population mortality patterns, followed by the influence of other socioeconomic factors, with geographical environmental factors having a relatively smaller impact.

Multilevel Longitudinal Functional Principal Component Model.

Sensor devices, such as accelerometers, are widely used for measuring physical activity (PA). These devices provide outputs at fine granularity (e.g., 10-100Hz or minute-level), which while providing rich data on activity patterns, also pose computational challenges with multilevel densely sampled data, resulting in PA records that are measured continuously across multiple days and visits. On the other hand, a scalar health outcome (e.g., BMI) is usually observed only at the individual or visit level. This leads to a discrepancy in numbers of nested levels between the predictors (PA) and outcomes, raising analytic challenges. To address this issue, we proposed a multilevel longitudinal functional principal component analysis (mLFPCA) model to directly model multilevel functional PA inputs in a longitudinal study, and then implemented a longitudinal functional principal component regression (FPCR) to explore the association between PA and obesity-related health outcomes. Additionally, we conducted a comprehensive simulation study to examine the impact of imbalanced multilevel data on both mLFPCA and FPCR performance and offer guidelines for selecting optimal methods.

Concurrent Functional Linear Regression Via Plug-in Empirical Likelihood

AbstractFunctional data with non-smooth features (e.g., discontinuities in the functional mean and/or covariance) and monotonicity arise frequently in practice. This paper develops simultaneous inference for concurrent functional linear regression in this setting. We construct a simultaneous confidence band for a functional covariate effect of interest. Along with a Wald-type formulation, our approach is based on a powerful nonparametric likelihood ratio method. Our procedures are flexible enough to allow discontinuities in the coefficient functions and the covariance structure, while accounting for discretization of the observed trajectories under a fixed dense design. A simulation study shows that the proposed likelihood ratio-based procedure outperforms the Wald-type procedure in moderate sample sizes. We apply the proposed methods to studying the effect of age on the occupation time curve derived from wearable device data obtained in an NHANES study.

Functional quantile regression with missing data in reproducing kernel Hilbert space

We, in this article, focus on functional partially linear quantile regression, where the observations are missing at random, which allows the response or covariates or response and covariates simultaneously missing. Estimation of the unknown function is done based on reproducing kernel method. Under suitable assumptions, we discuss consistency with rates of the estimators, and establish asymptotic normality of the estimator for the parameter. At the same time, we study hypothesis test of the parameter, and prove asymptotic distributions of restricted estimators of the parameter and test statistic under null hypothesis and local alternative hypothesis, respectively. Also, we study variable selection of the linear part of the model. By simulation and real data, finite sample performance of the proposed methods is analyzed.

On function-on-function linear quantile regression

We present two innovative functional partial quantile regression algorithms designed to accurately and efficiently estimate the regression coefficient function within the function-on-function linear quantile regression model. Our algorithms utilize functional partial quantile regression decomposition to effectively project the infinite-dimensional response and predictor variables onto a finite-dimensional space. Within this framework, the partial quantile regression components are approximated using a basis expansion approach. Consequently, we approximate the infinite-dimensional function-on-function linear quantile regression model using a multivariate quantile regression model constructed from these partial quantile regression components. To evaluate the efficacy of our proposed techniques, we conduct a series of Monte Carlo experiments and analyze an empirical dataset, demonstrating superior performance compared to existing methods in finite-sample scenarios. Our techniques have been implemented in the ffpqr package in .

Estimation in functional partially linear spatial autoregressive model

Functional regression has been a hot topic in statistical research. However, not much work has been done when response variables are cross-sectionally dependent variables and explanatory variables contain a real-valued scalar variable and a functional-valued random variable. In this paper, we consider a new functional partially linear spatial autoregressive model. Based on the functional principal components analysis and basis function approximation, we obtain the estimators of the unknown parameter and functions through the instrumental variables estimation method. The asymptotic normality and convergence rates of estimators are proved under some mild conditions. In addition, we illustrate the finite sample performance of the proposed estimation method through simulation study and a real data analysis.

Composite quantile estimation in partially functional linear regression model with randomly censored responses

Composite quantile estimation in partially functional linear regression model with randomly censored responses