Journal of the Korean Statistical Society

  • 제24권1호
  • /
  • Pages.233-242
  • /
  • 1995
  • /
  • 1226-3192(pISSN)
  • /
  • 2005-2863(eISSN)
한국통계학회 (The Korean Statistical Society)
권호 표지

Existence and Uniquenecess of the Smoothest Density with Prescribed Moments

  • Hong, Chang-Kon (Department of Statistics, Pusan National University, Pusan 609-735) ;
  • Kim, Choong-Rak (Department of Statistics, Pusan National University, Pusan 609-735)
  • 발행 : 1995.06.01
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

In this paper we will prove the existence and uniqueness of the smoothest density with prescribed moments. The space of functions considered is the Sobolev space $W^2_m[0,1]$ and the target functional to be minimized is the seminorm $$\mid$$\mid$f^{(m)}$\mid$$\mid$_{L^2}$, which measures the roughness of the function f.

키워드

참고문헌

  1. Sobolev Spaces Adams,R.A.
  2. Fizmatgiz, Moscow ; English Transl., MR 27 #4028;32 #1518 The Classical Moment Problem and Some Related Topics in Analysis Akhiezer,N.I.
  3. American Mathematical Society:Transactions v.68 Theory of reproducing kernels Aronszajn,N.
  4. Philosophical Magazine, 5th series v.21 The law of error and the elimination of chance Edgeworth,F.Y.
  5. Philosophical Magazine, 5th series v.24 The emphirical proof of the law of error Edgeworth,F.Y.
  6. Spline Smoothing and Nonparametric Regression Eubank,R.L.
  7. Translations of Mathematical Monographs v.50 The Markov Problem and Extremal Problems Krein,M.G.;Nudel'man,A.A.
  8. Memoires de l'Academie des Sciences de St-Petersburg, classe physicomathematique v.6 no.8;5 Sur les valeurs extremes des integrales et l'interpolation Markov,A.A.
  9. Philosophical Transactions of the Royal Society of London(A);Page references are to the reprint in Pearson v.185;1956 Contributions to the mathematical theory of evolution Pearson,K.
  10. Annales Scientifiques de I'Ecold Normale Superieure v.1 no.3 Quelques recherches sur les quadratures dites mecaniques Stieltjes,T.J.
  11. SIAM Nonparametric Function Estimation, Modeling, and Simulation Tapia,J.R.;Thompson,R.A.
  12. Journal des Mathematiques pures et eppliquees;Collected Papers v.19;2 no.2;10 Sur les valeurs limits des integrales Tchebycheff,P.
  13. CBMS 59;SIAM Spline Models for Observational Data Wahba,G.
  14. Functional Analysis(3rd edition) Yoshida,K.