Journal of the Korean Statistical Society

The Korean Statistical Society (한국통계학회)
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An Algorithm for One-Sided Generalized Least Squares Estimation and Its Application

  • Park, Chul-Gyu (Department of Applied Statistics, The University of Suwon, Suwon, 445-743)
  • Published : 2000.09.01
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Abstract

A simple and efficient algorithm is introduced for generalized least squares estimation under nonnegativity constraints in the components of the parameter vector. This algorithm gives the exact solution to the estimation problem within a finite number of pivot operations. Besides an illustrative example, an empirical study is conducted for investigating the performance of the proposed algorithm. This study indicates that most of problems are solved in a few iterations, and the number of iterations required for optimal solution increases linearly to the size of the problem. Finally, we will discuss the applicability of the proposed algorithm extensively to the estimation problem having a more general set of linear inequality constraints.

Keywords

References

  1. Journal of the American Statistical Association v.67 The isotonic regression problem and its dual Barlow, R.E.;Brunk, H.D.
  2. Biometrika v.46 A test of homogeneity for ordered alternatives Bartholomew, D.J.
  3. Journal of the Royal Statistical Society v.Seroes B no.23 A test of homogeneity of means under restricted alternatives(with discussions) Bartholomew, D.J.
  4. Linear Programming and Network Flows Bazara, M.S.;Jarvis, J.J.
  5. Annals of Mathematical Statistics v.26 Maximum likelihood estimates of monotone parameters Brunk, H.D.
  6. Journal of the American Statistical Association v.78 An algorithm for restricted least squares regression Dykstra, R.L.
  7. Statistics and Probability Letters v.11 Multinomial estimation procedures for isotonic cones Dykstra, R.L.;Lee, C.I.C.
  8. Annals of Statistics v.10 Order Restricted Statistical Tests on Multinomial and Poisson Parameters: The Starshaped Restriction Dykstra, R.L.;Robertson, T.
  9. Statistics and Probability Letters v.29 Restricted product multinomial and product Poisson maximum likelihood estimation based upon Fenchel duality El Barmi, H.;Dykstra, R.L.
  10. Biometrika v.50 A multivariate analogue of the one-sided test Kudo, A.
  11. Optimization by Vector Space Methods Luenberger, D.G.
  12. Linear and Nonlinear Programming Luenberger, D.G.
  13. Linear and Nonlinear Programming Luenberger, D.G.
  14. Statistics and Probability Letters v.37 Least squares estimation of two functios under order restriction in isotonicity Park, C.G.
  15. Order Restricted Statistical Inference Robertson, T.;Wright, F.T. & Dykstra, R.L.
  16. Biometrika v.70 A multivariate version of isotonic regression Sasabuchi, S.;Inutsuka, M.;Kulatunga, D.D.S.
  17. Applied Statistics v.36 Minimizing linear inequality constrained Mahalanobis distances Wollan, P.C.;Dykstra, R.L.