Nonparametric Homogeneity Test for Small Samples and Its Applications to COVID-19 Epidemic Curves Forecasting

The COVID-19 pandemic is accompanied by intensive attempts to build mathematical models to predict it. For this, various models are used, both traditional differential equations and machine learning models. Classical epidemiological compartment models contain parameters that are difficult to measure. Their results are used to model various scenarios, but it is difficult to obtain a reliable forecast with their help. Machine learning models, on the other hand, do not use prior assumptions, and their inferences are based only on training samples. This usually results in more reliable forecasts. In both the first and second cases, it is necessary not only to estimate the forecast error, but to compare the prediction accuracy of different models by checking the error homogeneity also. An additional factor complicating the problem is the small size of available samples in some cases. This forces one to resort to resampling methods. The article describes the Klyushin-Petunin test for testing the homogeneity of samples with ties in a multi-sample design and compares it with the traditional Anderson-Darling, Kruskal-Wallis and Friedman tests using the example of three methods for predicting the COVID-19 epidemic in the basis of epidemic data in Germany, Japan, South Korea and Ukraine.