# Hypothesis Testing in Nonlinear Function on Scalar Regression with Application to Child Growth Study

## TL;DR

This paper introduces a kernel machine-based hypothesis testing method for nonlinear function-on-scalar regression, applied to child growth data to assess the impact of toxic metals and methylation regions.

## Contribution

It develops a novel variance component test within a kernel machine framework for nonlinear function-on-scalar regression models.

## Key findings

- Method effectively detects associations in simulation studies.
- Application to NEST data reveals significant links between exposures and child growth.
- Provides a flexible approach for nonlinear functional data analysis.

## Abstract

We propose a kernel machine based hypothesis testing procedure in nonlinear function-on-scalar regression model. Our research is motivated by the Newborn Epigenetic Study (NEST) where the question of interest is whether a pre-specified group of toxic metals or methylation at any of 9 differentially methylated regions (DMRs) is associated with child growth. We take the child growth trajectory as the functional response, and model the toxic metal measurements jointly using a nonlinear function. We use a kernel machine approach to model the unknown function and transform the hypothesis of no effect to an appropriate variance component test. We demonstrate our proposed methodology using a simulation study and by applying it to analyze the NEST data.