Communications for Statistical Applications and Methods

  • 제15권5호
  • /
  • Pages.675-685
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  • 2008
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  • 2287-7843(pISSN)
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  • 2383-4757(eISSN)
한국통계학회 (The Korean Statistical Society)
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Sequential Shape Modification for Monotone Convex Function: L2 Monotonization and Uniform Convexifiation

  • Lim, Jo-Han (Department of Statistics, Seoul National University) ;
  • Lee, Sung-Im (Department of Statistics, Dankook University)
  • 발행 : 2008.09.30
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초록

This paper studies two sequential procedures to estimate a monotone convex function using $L_2$ 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.

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참고문헌

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