A Simple new algorithm for quadratic programming with applications in statistics

Communications in Statistics: Simulation and Computation

Volumn 42, Issue 5, 2013, Pages 1126-1139

  Meyer, Mary C ^a  

^a Department of Environmental and Radiological Health Sciences   (United States)

Author keywords

Cone projection; Constrained parameter estimation; Dual algorithm; Inequality constraints; Polar cone; Primal dual methods; Restricted least squares; Shape restricted regression

Indexed keywords

DUAL ALGORITHM; INEQUALITY CONSTRAINT; LEAST SQUARE; POLAR CONES; PRIMAL-DUAL METHODS; SHAPE-RESTRICTED REGRESSION;

CONES; CONSTRAINT THEORY; LEAST SQUARES APPROXIMATIONS; PARAMETER ESTIMATION; PROBLEM ORIENTED LANGUAGES;

ALGORITHMS;

EID: 84872023005     PISSN: 03610918     EISSN: 15324141     Source Type: Journal    
DOI: 10.1080/03610918.2012.659820     Document Type: Article

References (26)

1. Brunk, H. D. (1955).Maximum likelihood estimates of monotone parameters. Annals ofMathematical Statistics 26(4):607-616.
2. De Boor, C. (2001). A Practical Guide to Splines. Rev. ed. New York: Springer.
3. Dykstra, R. J. (1983). An algorithm for restricted least squares regression. Journal of the American Statistical Association 78:837-842.
4. Fang, S. C., Puthenpura, S. (1993). Linear Optimization and Extensions. Theory and Algorithms. Englewood Cliffs NJ: Prentice Hall.
5. Fraser, D. A. S., Massam, H. (1989). A mixed primal-dual bases algorithm for regression under inequality constraints. Application to convex regression. Scandinavian Journal of Statistics 16:65-74.
6. Goldfarb,D., Idnani,A. (1983).Anumerically stable dualmethod for solving strictly convex quadratic programs. Mathematical Programming 27:1-33.
7. Gouríeroux, C., Holly, A., Monfort, A. (1982). Likelihood ratio test, Wald test, and Kuhn-Tucker test in linear models with inequality constraints on the regression parameters. Econometrica 50(1):63-80.
8. Gourieroux, C., Monfort, A. (1995). Statistics and Econometric Models. Cambridge: Cambridge University Press.
9. Gromping, U. (2010). Inference with linear equality and inequality constraints using R: The package ic.infer. Journal of Statistical Software 33(10):1-31.
10. Hawkins, D. M. (1994). Fitting monotonic polynomials to data. Computational Statistics 9:233-247.
11. Judge, G. G., Takayama, T. (1966). Inequality restrictions in regression analysis. Journal of the American Statistical Association 61:166-181.
12. Karmarkar, N. (1984). A new polynomial time algorithm for linear programming. Combinatorica 4:373-395.
13. Lawson, C. L., Hanson, R. J. (1974). Solving Least Squares Problems. Englewood Cliffs NJ: Prentice Hall.
14. Liew, C. K. (1976). Inequality constrained least-squares estimation. Journal of the American Statistical Association 71:746-751.
15. McCullagh, P., Nelder, J. A. (1989). Generalized Linear Models. 2nd ed. New York: Chapman & Hall.
16. Meyer, M. C. (1999). An extension of the mixed primal-dual bases algorithm to the case of more constraints than dimensions. Journal of Statistical Planning and Inference 81:13-31.
17. Meyer, M. C. (2008). Inference using shape-restricted regression splines. Annals of Applied Statistics 2(3):1013-1033.
18. Meyer, M. C., Woodroofe, M. (2004). Estimation of a unimodal density using shape restrictions. Canadian Journal of Statistics 32(1):85-100.
19. Ramsay, J. O. (1988). Monotone regression splines in action. Statistical Science 3(4):425-461.
20. Raubertas, R. F., Lee, C. I. C., Nordheim, E. V. (1986). Hypothesis tests for normalmeans constrained by linear inequalities. Communications in Statistics - Theory and Methods 15(9):2809-2833.
21. Robertson, T.,Wright, F. T., Dykstra, R. L. (1988). Order Restricted Statistical Inference. NewYork: Wiley.
22. Ruppert, D., Wand, M. P., Carroll, R. J. (2003). Semiparametric Regression (Cambridge Series in Statistical and Probabilistic Mathematics). Cambridge: Cambridge University Press.
23. Silvapulle, M. J. (1994). On tests against one-sided hypotheses in some generalized linear models. Biometrics 50(3):853-858.
24. Silvapulle, M. J., Sen, P. K. (2005). Constrained Statistical Inference. New York: Wiley.
25. Van Eeden, C. (2006). Restricted Parameter Space Estimation Problems. New York: Springer.
26. Wilhelmsen, D. R. (1976). A nearest point algorithm for convex polyhedral cones and applications to positive linear approximation. Mathematics of Computation 30(133):48-57.