Search for: All records

Summary Object-oriented data analysis is a fascinating and evolving field in modern statistical science, with the potential to make significant contributions to biomedical applications. This statistical framework facilitates the development of new methods to analyze complex data objects that capture more information than traditional clinical biomarkers. This paper applies the object-oriented framework to analyze physical activity levels, measured by accelerometers, as response objects in a regression model. Unlike traditional summary metrics, we utilize a recently proposed representation of physical activity data as a distributional object, providing a more nuanced and complete profile of individual energy expenditure across all ranges of monitoring intensity. A novel hybrid Fréchet regression model is proposed and applied to US population accelerometer data from National Health and Nutrition Examination Survey (NHANES) 2011 to 2014. The semi-parametric nature of the model allows for the inclusion of nonlinear effects for critical variables, such as age, which are biologically known to have subtle impacts on physical activity. Simultaneously, the inclusion of linear effects preserves interpretability for other variables, particularly categorical covariates such as ethnicity and sex. The results obtained are valuable from a public health perspective and could lead to new strategies for optimizing physical activity interventions in specific American subpopulations. 

Estimation of the mean and covariance parameters for functional data is a critical task, with local linear smoothing being a popular choice. In recent years, many scientific domains are producing multivariate functional data for which $$p$$, the number of curves per subject, is often much larger than the sample size $$n$$. In this setting of high-dimensional functional data, much of developed methodology relies on preliminary estimates of the unknown mean functions and the auto- and cross-covariance functions. This paper investigates the convergence rates of local linear estimators in terms of the maximal error across components and pairs of components for mean and covariance functions, respectively, in both $L^2$ and uniform metrics. The local linear estimators utilize a generic weighting scheme that can adjust for differing numbers of discrete observations $$N_{ij}$$ across curves $$j$$ and subjects $$i$$, where the $$N_{ij}$$ vary with $$n$$. Particular attention is given to the equal weight per observation (OBS) and equal weight per subject (SUBJ) weighting schemes. The theoretical results utilize novel applications of concentration inequalities for functional data and demonstrate that, similar to univariate functional data, the order of the $$N_{ij}$$ relative to $$p$$ and $$n$$ divides high-dimensional functional data into three regimes (sparse, dense, and ultra-dense), with the high-dimensional parametric convergence rate of $$\left\{\log(p)/n\right\}^{1/2}$$ being attainable in the latter two.