Regularized tessellation density estimation with bootstrap aggregation and complexity penalization

Locally adaptive density estimation presents challenges for parametric or non-parametric estimators. Several useful properties of tessellation density estimators (TDEs), such as low bias, scale invariance and sensitivity to local data morphology, make them an attractive alternative to standard kernel techniques. However, simple TDEs are discontinuous and produce highly unstable estimates due to their susceptibility to sampling noise. With the motivation of addressing these concerns, we propose applying TDEs within a bootstrap aggregation algorithm, and incorporating model selection with complexity penalization. We implement complexity reduction of the TDE via sub-sampling, and use information-theoretic criteria for model selection, which leads to an automatic and approximately ideal bias/variance compromise. The procedure yields a stabilized estimator that automatically adapts to the complexity of the generating distribution and the quantity of information at hand, and retains the highly desirable properties of the TDE. Simulation studies presented suggest a high degree of stability and sensitivity can be obtained using this approach.