ON MINIMAX RISK OF NON-SMOOTH FUNCTIONAL, ITS ASYMPTOTIC PROPERTIES AND POLYNOMIAL ESTIMATION

  • MOSES KOLOLI MUKHWANA
  • ROMANUS O. OTIENO
  • ORWA O. GEORGE
  • MUNG’ATU K. JOSEPH
  • N. B. OKELO
DOI: https://doi.org/10.53555/m.v1i2.2406

Abstract

Nonparametric estimation of non-smooth functionals deals with highly structured
problems which arise, modeled or cast differently from the ones for which
mainline numerical methods have been designed. Non-smooth functional
estimation problems show some features that are different from those of estimating
smooth functionals. This is in terms of the optimal rates of convergence as well as
the technical tools needed for the analysis of the MiniMax lower bounds and the
construction of the optimal estimators. The main difficulty of estimating the nonsmooth functionals is traced back to the non differentiability of the absolute value
function at the origin. This is reflected both in the derivation of the lower bounds
and the construction of optimal estimators. The construction of the optimal
estimators of the non-smooth functionals is more complicated than those for linear
and quadratic functionals. In this study we consider asymptotic properties,
polynomial estimation and MiniMax risk involving non-smooth functionals.

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Author Biographies

ROMANUS O. OTIENO

DEPARTMENT OF STATISTICS AND ACTUARIAL SCIENCES,
JOMO KKENYATTA UNIVERSITY OF AGRICULTURE AND
TECHNOLOGY, KENYA

ORWA O. GEORGE

DEPARTMENT OF STATISTICS AND ACTUARIAL SCIENCES,
JOMO KKENYATTA UNIVERSITY OF AGRICULTURE AND
TECHNOLOGY, KENYA

MUNG’ATU K. JOSEPH

DEPARTMENT OF STATISTICS AND ACTUARIAL SCIENCES,
JOMO KKENYATTA UNIVERSITY OF AGRICULTURE AND
TECHNOLOGY, KENYA

N. B. OKELO

SCHOOL OF MATHEMATICS AND ACTUARIAL SCIENCE,
JARAMOGI OGINGA ODINGA UNIVERSITY OF SCIENCE AND TECHNOLOGY,
P. O. BOX 210-40601, BONDO-KENYA

Published
2015-06-30
How to Cite
MUKHWANA, M. K., OTIENO, R. O., GEORGE, O. O., JOSEPH, M. K., & OKELO, N. B. (2015). ON MINIMAX RISK OF NON-SMOOTH FUNCTIONAL, ITS ASYMPTOTIC PROPERTIES AND POLYNOMIAL ESTIMATION. IJRDO -JOURNAL OF MATHEMATICS, 1(2), 18-25. https://doi.org/10.53555/m.v1i2.2406
Issue
Vol. 1 No. 2 (2015): IJRDO-Journal of Mathematics
Section
Articles

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