Sampling of highly correlated data for polynomial regression and model discovery

The usual way of conducting empirical comparisons among competing polynomial model selection criteria is by generating artificial data from created true models with specified link weights. The robustness of each model selection criterion is then judged by its ability to recover the true model from its sample data sets with varying sizes and degrees of noise.

If we have a set of multivariate real data and have empirically found a polynomial regression model that is so far seen as the right model represented by the data, we would like to be able to replicate the multivariate data artificially to enable us to run multiple experiments to achieve two objectives. First, to see if the model selection criteria can recover the model that is seen to be the right model. Second, to find out the minimum sample size required to recover the right model.

This paper proposes a methodology to replicate real multivariate data using its covariance matrix and a polynomial regression model seen as the right model represented by the data. The sample data sets generated are then used for model discovery experiments.