# Inference For High-Dimensional Split-Plot-Designs: A Unified Approach for Small to Large Numbers of Factor Levels

## TL;DR

This paper develops robust inference procedures for high-dimensional split-plot designs with many factors and groups, applicable in life sciences where large numbers of observations per subject are common.

## Contribution

It introduces a unified approach for inference in heteroscedastic split-plot designs with high-dimensional data, extending classical methods to handle increasing dimensions and groups.

## Key findings

- Procedures are robust against increasing dimensions and groups.
- Limit distributions are characterized in a general asymptotic framework.
- Small sample approximations improve inference accuracy.

## Abstract

Statisticians increasingly face the problem to reconsider the adaptability of classical inference techniques. In particular, divers types of high-dimensional data structures are observed in various research areas; disclosing the boundaries of conventional multivariate data analysis. Such situations occur, e.g., frequently in life sciences whenever it is easier or cheaper to repeatedly generate a large number $d$ of observations per subject than recruiting many, say $N$, subjects. In this paper we discuss inference procedures for such situations in general heteroscedastic split-plot designs with $a$ independent groups of repeated measurements. These will, e.g., be able to answer questions about the occurrence of certain time, group and interactions effects or about particular profiles. The test procedures are based on standardized quadratic forms involving suitably symmetrized U-statistics-type estimators which are robust against an increasing number of dimensions $d$ and/or groups $a$. We then discuss its limit distributions in a general asymptotic framework and additionally propose improved small sample approximations. Finally its small sample performance is investigated in simulations and the applicability is illustrated by a real data analysis.