Ufuk Beyaztas

This paper introduces a novel spatial scalar‐on‐function (SoF) quantile regression model that extends classical SoF models to account for spatial dependence and heterogeneous conditional distributions. The proposed model incorporates spatial autocorrelation through a spatially lagged response and characterises the entire conditional distribution of a scalar outcome given a functional predictor. To address endogeneity induced by the spatial lag term, we develop two robust estimation procedures based on instrumental variable (IV) strategies. The ‐consistency and asymptotic normality of the proposed estimators are established under mild regularity conditions. We demonstrate through extensive Monte Carlo simulations that the proposed estimators outperform existing mean‐based and robust alternatives, particularly in settings with strong spatial dependence and outlier contamination. We apply our method to high‐resolution environmental data from the Lombardy region in Italy, using daily ozone trajectories to predict daily mean concentrations of particulate matter with a diameter of less than 2.5 micrometers. The empirical results confirm the superiority of our approach in predictive accuracy, robustness and interpretability at various quantile levels. Our method has been implemented in the ssofqrm package.

The function-on-function regression model is fundamental for analyzing relationships between functional covariates and responses. However, most existing function-on-function regression methodologies assume independence between observations, which is often unrealistic for spatially structured functional data. We propose a novel penalized spatial function-on-function regression model to address this limitation. Our approach extends the generalized spatial two-stage least-squares estimator to functional data, while incorporating a roughness penalty on the regression coefficient function using a tensor product of B-splines. This penalization ensures optimal smoothness, mitigating overfitting, and improving interpretability. The proposed penalized spatial two-stage least-squares estimator effectively accounts for spatial dependencies, significantly improving estimation accuracy and predictive performance. We establish the asymptotic properties of our estimator, proving its $\sqrt{n}$-consistency and asymptotic normality under mild regularity conditions. Extensive Monte Carlo simulations demonstrate the superiority of our method over existing non-penalized estimators, particularly under moderate to strong spatial dependence. In addition, an application to North Dakota weather data illustrates the practical utility of our approach in modeling spatially correlated meteorological variables. Our findings highlight the critical role of penalization in enhancing robustness and efficiency in spatial function-on-function regression models. To implement our method we used the \texttt{robflreg} package on CRAN.

Despite extensive research on life-extending interventions, rigorous statistical techniques to determine their impact on compression of morbidity (CoM) are rarely used. We present a case example of an analytical method for examining the effect of life-extending dietary interventions on CoM by comparing the rates of decline in vitality and survival toward the end of life. Using data from previous experimental studies in mice, we calculated the average rate of vitality decline by fitting exponential decay models to individual vitality trajectories and compared this rate with the rate of survival decline estimated from Cox proportional hazards model. The results showed that, surprisingly, the life-extending interventions failed to compress morbidity. Instead, the models suggested a potential expansion of morbidity with the interventions, particularly for chronic caloric restriction, as evidenced by a greater difference between the rates of vitality decline and survival decline in the intervention group than in the control group. The results further showed age-dependent effects, with interventions likely to demonstrate CoM at very old ages. These findings challenge the assumption that lifespan extension necessarily compresses morbidity, highlighting the need to consider lifespan, healthspan, and CoM as endpoints when evaluating anti-aging interventions. We do not claim that life-extending interventions categorically fail to achieve CoM; rather, we demonstrate how a rigorous statistical approach can be applied to test the CoM hypothesis. Our framework offers a valuable tool for future studies, and further refining this method will be crucial to determine under which circumstances lifespan extension leads to CoM. The potential to choose from multiple analyses of CoM calls for leadership in the geroscience community both to standardize the nomenclature so that different CoM analysis approaches can be communicated clearly and to establish a “default” CoM analysis for everyone to use in addition to their analyses of choice, thus facilitating comparisons and meta-analyses across studies.

This paper introduces a novel spatial scalar-on-function quantile regression model that extends classical scalar-on-function models to account for spatial dependence and heterogeneous conditional distributions. The proposed model incorporates spatial autocorrelation through a spatially lagged response and characterizes the entire conditional distribution of a scalar outcome given a functional predictor. To address the endogeneity induced by the spatial lag term, we develop two robust estimation procedures based on instrumental variable strategies. $\sqrt{n}$-consistency and asymptotic normality of the proposed estimators are established under mild regularity conditions. We demonstrate through extensive Monte Carlo simulations that the proposed estimators outperform existing mean-based and robust alternatives, particularly in settings with strong spatial dependence and outlier contamination. We apply our method to high-resolution environmental data from the Lombardy region in Italy, using daily ozone trajectories to predict daily mean particulate matter with a diameter of less than 2.5 micrometers concentrations. The empirical results confirm the superiority of our approach in predictive accuracy, robustness, and interpretability across various quantile levels. Our method has been implemented in the \texttt{ssofqrm} R package.

Functional logistic regression is a popular model to capture a linear relationship between binary response and functional predictor variables. However, many methods used for parameter estimation in functional logistic regression are sensitive to outliers, which may lead to inaccurate parameter estimates and inferior classification accuracy. We propose a robust estimation procedure for functional logistic regression, in which the observations of the functional predictor are projected onto a set of finite-dimensional subspaces via robust functional principal component analysis. This dimension-reduction step reduces the outlying effects in the functional predictor. The logistic regression coefficient is estimated using an M-type estimator based on binary response and robust principal component scores. In doing so, we provide robust estimates by minimizing the effects of outliers in the binary response and functional predictor variables. Via a series of Monte-Carlo simulations and using hand radiograph data, we examine the parameter estimation and classification accuracy for the response variable. We find that the robust procedure outperforms some existing robust and non-robust methods when outliers are present, while producing competitive results when outliers are absent. In addition, the proposed method is computationally more efficient than some existing robust alternatives.