Abstract: Kriging models are popular in analyzing computer experiments. The most widely used kriging models apply a constant mean to capture the overall trend. This method can lead to a poor prediction when strong trends exist. To tackle this problem, a new modeling method is proposed, which incorporates a variable selection mechanism into kriging via a penalty function. An efficient algorithm is introduced and oracle properties in terms of selecting the correct mean function are derived according to fixed-domain asymptotics. The finite-sample performance is examined via a simulation study. Application of the proposed methodology to circuit-simulation experiments demonstrates a remarkable improvement in prediction, and the capability of identifying variables that most affect the system.
Key words and phrases: Computer model, fixed-domain asymptotics, Gaussian process model, geostatistics, oracle procedure, variable selection.