Variational solution of penalized likelihood problems and smooth curve estimation

• 成果类型: Article
• 署名作者: Machler, MB
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1176324309
• 发表日期: 1995
• 页码: 1496-1517
• 关键词: spline functions; regression

摘要

Usual nonparametric regression estimators often show many little wiggles which do not appear to be necessary for a good description of the data. The new ''Wp'' smoother is a maximum penalized likelihood (MPL) estimate with a novel roughness penalty. It penalizes a relative change of curvature. This leads to disjoint classes of functions, each with a given number, n(w), of inflection points. For a ''Wp'' estimate, f ''(x) = +/- (x - w(1))...(x - w(nw)). exp h(f)(x), which is semiparametric, with parameters w(j) and nonparametric part h(f)(.). The main mathematical result is a convenient form of the characterizing differential equation for a very general class of MPL estimators.