Journal of the Korean Statistical Society

  • 제26권1호
  • /
  • Pages.23-30
  • /
  • 1997
  • /
  • 1226-3192(pISSN)
  • /
  • 2005-2863(eISSN)
한국통계학회 (The Korean Statistical Society)
권호 표지

Maximum Penalized Likelihood Estimate in a Sobolev Space

  • Park, Young J. (Research Institute of Statistics, Seoul National University, Seoul, 151-742) ;
  • Lee, Young H. (Department of Mathematic Education, Ewha Womens University, Seoul, 120-750)
  • 발행 : 1997.03.01
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초록

We show that the Maximum Penalized Likelihood Estimate uniquely exits in a Sobolve spece which consists of bivariate density functions. The Maximum Penalized Likehood Estimate is represented as the square of the sum of the solutions of the Modified Helmholtz's equation on the compact subset of R$^{2}$.

키워드

참고문헌

  1. Mathematical Methods for Physicists Arfken, G.
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  3. Biometrica v.58 Nonparametric roughness penalties for probability density Good, I.J.;Gaskin, R.A.
  4. Journal of the American Statistical Association v.86 recent Developments in Nonparametric Density Estimation Izenman, A.J.
  5. Density Estimation for Statistics and Data Analysis Silverman, B.W.
  6. Nonparametric Probability Density Estimation Tapia, R.A.;Thompson, J.R.
  7. Journal of the American Statistical Association v.78 Splines in Statistics Wegman, E.J.;Wright, I. W.