Efficient estimation of smoothing spline with exact shape constraints
作者机构：Department of StatisticsUniversity of Wisconsin-MadisonMadisonWIUSA Department of StatisticsVirginia TechBlacksburgVAUSA
出 版 物：《Statistical Theory and Related Fields》 (统计理论及其应用（英文）)
年 卷 期：2021年第5卷第1期
页 面：55-69页
学科分类：07[理学] 0714[理学-统计学（可授理学、经济学学位）] 0701[理学-数学] 0812[工学-计算机科学与技术（可授工学、理学学位）] 070101[理学-基础数学]
基 金：supported by National Science Foundation
主 题：Monotonicity non-linear constraint non-parametric regression
摘 要：Smoothing spline is a popular method in non-parametric function *** the analysis of data from real applications,specific shapes on the estimated function are often required to ensure the estimated function undeviating from the domain *** this work,we focus on constructing the exact shape constrained smoothing spline with efficient ***‘exact’here is referred as to impose the shape constraint on an infinite set such as an interval in one-dimensional *** the estimation becomes a so-called semi-infinite optimisation problem with an infinite number of *** proposed method is able to establish a sufficient and necessary condition for transforming the exact shape constraints to a finite number of constraints,leading to efficient estimation of the shape constrained *** performance of the proposed methods is evaluated by both simulation and real case studies.
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