Valid hypothesis testing in face of spatially dependent data using multi-layer perceptrons and sub-sampling techniques

Feedforward multi-layer perceptrons (MLPs) are valuable modeling tools when considered as non-linear regression technique. MLPs are employed to estimate a priori unknown relationships between a response variable and regressors. Their estimates can serve as a basis for statistical inference. Hypotheses are more substantial and appropriate than those within reach of more traditional methods. This is due to the ability to extract complex non-linear interactive effects. The methodology of drawing valid statistical inference by MLPs in the context of spatially dependent heteroscedastic data is provided. The approach is data-driven and computationally feasible. The appropriateness and suitability of the procedure is demonstrated with an artificial data set and a practical application. Three-layer feedforward networks are applied to approximate the data-generating process. In context of spatially correlated residuals, a suitable statistic is given to test if a specific input variable is predictive of the response variable. Finally, sub-sampling techniques are adopted to arrive at valid statistical conclusions.