Journal of the Korean Statistical Society

The Korean Statistical Society (한국통계학회)
권호 표지

Characterization of the Smoothest Density with Given Moments

  • Hong, Changkon (Department of Statistics, Pusan National University)
  • Published : 2001.09.01
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, we characterize the smoothest density with prescribed moments. Hong and Kim(1995) proved the existence and uniqueness of such as density. we introduce the general optimal control problem and prove some theorems on the characterization of the minimizer using the optimal control problem techniques.

Keywords

References

  1. Sobolev Spaces Adams, R.A
  2. The Classical Moment Problem and Some Related Topics in Analysis Akhiezer, N.I
  3. Functional Analysis Devito, C.L
  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 empirical proof of the law of error Edgeworth, F.Y
  6. Lecture Notes in Economics and Mathematical Systems v.67 Lectures on Mathematical Theory of Extremum Problems Girsanov, I.V
  7. Calculus of Variations and Optimal Control Theory Hestenes, M.R
  8. Journal of the Korean Statistical Society v.24 The existence and uniqueness of the smoothest density with prescribed moments Hong, C;Kim, C
  9. Lectures Notes in Economics and Mathematical System v.152 Notwendige Optimalitatsbedingungen und ihre Anwendung Kirsch, A;Warth, W;Werner, J
  10. Translations of Mathematical Monographs v.50 The Markov Problem and Extremal Problems Krein, M.G;Nudel'man, A.A
  11. Journal of Optimization Theory and Applications v.20 On the existence and nonexistence of Lagrange multipliers in Banach spaces Kurcyusz, S
  12. Optimization by Vector Space Methods Luenberger, D.G
  13. CWI Tract. v.53 Numerical Solution of Optimal Control Problems with State Constraints by Sequential Quadratic Programming in Function Space Machielsen, K.C.P
  14. Memoires de l'Academie des Science de St.-Petersburg, classe physico-mathematique v.8 no.6 Sur les valeurs extremes des integrales et l'interpolation Markov, A.A
  15. Philosophical Transactions of the Royal Society of London (A) v.185 Contributions to the mathematical theory of evolution Pearson, K
  16. Karl Pearson's Early Statistical Papers Pearson, K
  17. Annales Scientifiques de l'Ecold Normale Superieure v.1 no.3 Quelques recherches sur les quadratures dites mecaniques Stieltjes, T.J
  18. Journal des Mathematiques pures et eppliquees v.19 no.2 Sur les valeurs limits des integrales Tchebycheff, P
  19. Fundamental Principles of the Theory of Extremal Problems Tikhomirov, V.M