Multiple comparisons of polynomial regression models using simultaneous confidence bands

The problem of multiple comparisons is widespread and frequently encountered in practice. Zhou has been the first to investigate multiple comparisons of polynomial regression models using simultaneous confidence bands. However, Zhou’s method has limitations: it can only compare between quadratic polynomial regression models and between cubic polynomial regression models. The method cannot compare quadratic polynomial regression models with cubic polynomial regression models, nor can it compare between polynomial regression models of order higher than three. These limitations restrict its application scope. This study extends Zhou’s work by constructing a set of confidence bands that enables multiple comparisons between polynomial regression models of arbitrary orders. The simulation demonstrates that the proposed method is robust and widely applicable. Additionally, an example is included to illustrate its application in solving real-world problems.