Sequential Shape Modification for Monotone Convex Function: L2 Monotonization and Uniform Convexifiation

Title & Authors
Sequential Shape Modification for Monotone Convex Function: L2 Monotonization and Uniform Convexifiation
Lim, Jo-Han; Lee, Sung-Im;

Abstract
This paper studies two sequential procedures to estimate a monotone convex function using $\small{L_2}$ monotonization and uniform convexification; one, denoted by FMSC, monotonizes the data first and then, convexifis the monotone estimate; the other, denoted by FCSM, first convexifies the data and then monotonizes the convex estimate. We show that two shape modifiers are not commutable and so does FMSC and FCSM. We compare them numerically in uniform error(UE) and integrated mean squared error(IMSE). The results show that FMSC has smaller uniform error(UE) and integrated mean squared error(IMSE) than those of FCSC.
Keywords
Commutability;$\small{L_2}$ monotonization;monotone convex function;sequential estimation;uniform convexification;
Language
English
Cited by
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