University of California, Berkeley - Department of Statistics
Extended linear models form a very general framework for statistical modeling. Many practically important contexts fit into this framework, including regression, logistic or Poisson regression, density estimation, spectral density estimation, and conditional density estimation. Moreover, hazard regression, proportional hazard regression, marked counting process regression, and diffusion processes with or without jumps, all perhaps with time-dependent covariates, also fit into this framework. Polynomial splines and their tensor products provide a universal tool for constructing estimators for extended linear models. The theory on rates of convergence of such estimators as it applies both to fixed knot splines and to free knot splines will be surveyed, and the implications of this theory for the development of corresponding methodology will be discussed.