Nonasymptotic Analysis of the Lawley–Hotelling Statistic for High-Dimensional Data

We consider the General Linear Model (GLM) which includes multivariate analysis of variance (MANOVA) and multiple linear regression as special cases. In practice, there are several widely used criteria for GLM: Wilks’ lambda, Bartlett–Nanda–Pillai test, Lawley–Hotelling Roy maximum root test. Limiting distributions first three mentioned tests known under different asymptotic settings. present paper, we obtain computable error bounds normal approximation statistic when dimension grows proportionally to sample size. This result enables us get more precise calculations p-values in applications analysis. often analysts encounter situations where number factors is large comparable with Examples include medicine, biology (i.e., DNA microarray studies), finance.