arXiv subjects

Jennifer A. Schrack

Publications and source records attributed to Jennifer A. Schrack.

2 recordsLinked to original sources

arXiv2024

Distributional outcome regression via quantile functions and its application to modelling continuously monitored heart rate and physical activity

Modern clinical and epidemiological studies widely employ wearables to record parallel streams of real-time data on human physiology and behavior. With recent advances in distributional data analysis, these high-frequency data are now often treated as distributional observations resulting in novel regression settings. Motivated by these modelling setups, we develop a distributional outcome regression via quantile functions (DORQF) that expands existing literature with three key contributions: i) handling both scalar and distributional predictors, ii) ensuring jointly monotone regression structure without enforcing monotonicity on individual functional regression coefficients, iii) providing statistical inference via asymptotic projection-based joint confidence bands and a statistical test of global significance to quantify uncertainty of the estimated functional regression coefficients. The method is motivated by and applied to Actiheart component of Baltimore Longitudinal Study of Aging that collected one week of minute-level heart rate (HR) and physical activity (PA) data on 781 older adults to gain deeper understanding of age-related changes in daily life heart rate reserve, defined as a distribution of daily HR, while accounting for daily distribution of physical activity, age, gender, and body composition. Intriguingly, the results provide novel insights in epidemiology of daily life heart rate reserve.

stat.ME↗

arXiv2022

Shape-constrained Estimation in Functional Regression with Bernstein Polynomials

Shape restrictions on functional regression coefficients such as non-negativity, monotonicity, convexity or concavity are often available in the form of a prior knowledge or required to maintain a structural consistency in functional regression models. A new estimation method is developed in shape-constrained functional regression models using Bernstein polynomials. Specifically, estimation approaches from nonparametric regression are extended to functional data, properly accounting for shape-constraints in a large class of functional regression models such as scalar-on-function regression (SOFR), function-on-scalar regression (FOSR), and function-on-function regression (FOFR). Theoretical results establish the asymptotic consistency of the constrained estimators under standard regularity conditions. A projection based approach provides point-wise asymptotic confidence intervals for the constrained estimators. A bootstrap test is developed facilitating testing of the shape constraints. Numerical analysis using simulations illustrate improvement in efficiency of the estimators from the use of the proposed method under shape constraints. Two applications include i) modeling a drug effect in a mental health study via shape-restricted FOSR and ii) modeling subject-specific quantile functions of accelerometry-estimated physical activity in the Baltimore Longitudinal Study of Aging (BLSA) as outcomes via shape-restricted quantile-function on scalar regression (QFOSR). R software implementation and illustration of the proposed estimation method and the test is provided.

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