An orthogonal forward regression technique for sparse kernel density estimation

摘要: Using the classical Parzen window (PW) estimate as desired response, kernel density estimation is formulated a regression problem and orthogonal forward technique adopted to construct sparse (SKD) estimates. The proposed algorithm incrementally minimises leave-one-out test score select model, local regularisation method incorporated into construction process further enforce sparsity. weights of selected model are finally updated using multiplicative nonnegative quadratic programming algorithm, which ensures unity constraints for has ability reduce size further. Except width, no other parameters that need tuning, user not required specify any additional criterion terminate procedure. Several examples demonstrate this simple regression-based approach effectively SKD with comparable accuracy full-sample optimised PW estimate.