On non-normal asymptotic behavior of optimal solutions for stochastic programming problems and on related problems of mathematical statistics

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1. R. E. Barlow J. Bartholomew J. N. Bremner, H. D. Brunk, Statistical Inference under Order Restrictions: The Theory and Application of Isotonic Regression, J. Wiley, New York 1972. (1972) MR0326887
2. K. Behnen, G. Neuhaus, Rank Tests with Estimated Scores and Their Application, (Teubner Skripten zur Mathematischen Stochastik.) Teubner, Stuttgart 1989. (1989) Zbl0692.62041MR1003116
3. H. Chernoff, On the distribution of the likelihood ratio, Ann. Math. Statist. 25 (1954), 573-578. (1954) Zbl0056.37102MR0065087
4. R. Clarke, Optimization and Nonsmooth Analysis, Wiley Interscience, New York 1983. (1983) Zbl0582.49001MR0709590
5. J. Dupačová, Stability in stochastic programming with recourse: Contaminated distributions, Math. Programming Study 27 (1986), 133-144. (1986) MR0836754
6. J. Dupačová, Stochastic programming with incomplete information: A survey of results on postoptimization and sensitivity analysis, Optimization 18 (1987), 507-532. (1987) MR0909659
7. J. Dupačová, Asymptotic properties of restricted Li -estimates of regression, In: Statistical Data Analysis Based on Li-norm and Related Methods (Y. Dodge, ed.), North-Holland, Amsterdam 1987, pp. 263 - 274. (1987) MR0949231
8. J. Dupačová, On nonnormal asymptotic behavior of optimal solutions of stochastic programming problems: The parametric case, In: Proc. 4th Prague Symp. Asymptotic Statistics (P. Mandl, M. Huskova, eds.), Charles University, Prague 1989, pp. 205-214. (1989) MR1051439
9. J. Dupačová, On statistical sensitivity analysis in stochastic programming, Ann. Oper. Res. 29 (1990). (1990) MR1118898
10. J. Dupačová, R. J., B. Wets, Asymptotic behaviour of statistical estimators and of optimal solutions of stochastic optimization problems, Ann. Statist. 16 (1988), 1517-1549. (1988) MR0964937
11. V. Fiacco, J. Kyparisis, Sensitivity analysis in nonlinear programming under second order assumptions, In: Systems and Optimization (A. Bagich, H. Th. Jongen, eds.), Springer-Verlag, Berlin-Heidelberg-New York 1985, pp. 74-97. (1985) Zbl0573.90089MR0878584
12. J. Gauvin, A necessary and sufficient regularity condition to have bounded multipliers in nonconvex programming, Math. Programming 12 (1977), 136-138. (1977) Zbl0354.90075MR0489903
13. S. van de Geer, Asymptotic Normality of Minimum Li-norm Estimators in Linear Regression, Report MS-R8806 Centre for Mathematics and Computer Science, Amsterdam 1988. (1988) 
14. C. Gouriéroux A. Holly, A. Monfort, Likelihood ratio test, Wald test and KuhnTucker test in linear models with inequality constraints on the regression parameters, Econometrica 50 (1982), 63-80. (1982) MR0640166
15. P. J. Huber, Robust Statistics, J. Wiley, New York 1981. (1981) Zbl0536.62025MR0606374
16. K. Jittorntrum, Solution point differentability without strict complementarity in nonlinear programming, Math. Programming Study 21 (1984), 127-138. (1984) MR0751247
17. G. G. Judge, T. Takayama, Inequality restriction in regression analysis, J. Amer. Statist. Assoc. 67 (1966), 166-181. (1966) MR0193713
18. A. J. King, Asymptotic Behaviour of Solutions in Stochastic Optimization: Nonsmooth Analysis and the Derivation of Non-normal Limit Distribution, Ph. D. Dissertation, Univ. of Washington 1986. (1986) 
19. A. J. King, R. T. Rockafellar, Asymptotic theory for solutions in generalized M-estimation and stochastic programming, Preprint, 1989. (1989) 
20. M. Kojima, Strongly stable stationary solutions in nonlinear program, In: Analysis and Computation of Fixed Points (S. M. Robinson, ed.), Academic Press, New York 1980. (1980) MR0592631
21. J. Kyparisis, Sensitivity analysis for nonlinear programs and variational inequalities with nonunique multipliers, Math. Oper. Res. (to appear). Zbl0708.90086MR1051573
22. Ch. K. Liew, Inequality constrained Least-squares estimation, J. Amer. Statist. Assoc. 71 (1976), 746-751. (1976) Zbl0342.62037MR0428625
23. T. Robertson F. T. Wright, R. L. Dykstra, Order Restricted Statistical Inference (Wiley Series in Probability and Statistics), J. Wiley, New York 1988. (1988) MR0961262
24. S. M. Robinson, Local structure of feasible sets in nonlinear programming. Part III: Stability and sensitivity, Math. Programming Study 30 (1986), 45-66. (1986) MR0874131
25. S. M. Robinson, Local epi-continuity and local optimization, Math. Programming 37 (1987), 208-222. (1987) Zbl0623.90078MR0883021
26. R. J. Serfting, Approximation Theorems in Mathematical Statistics, J. Wiley, New York 1980. (1980) 
27. A. Shapiro, Sensitivity analysis of nonlinear programs and differentiability properties of metric projections, SIAM J. Control Optim. 26 (1988), 628-645. (1988) Zbl0647.90089MR0937676
28. A. Shapiro, Towards a unified theory of inequality constrained testing in multivariate analysis, Internat. Statist. Rev. 56 (1988), 49-62. (1988) Zbl0661.62042MR0963140
29. A. Shapiro, Asymptotic properties of statistical estimators in stochastic programming, Ann. Statist. 77(1989), 841-858. (1989) Zbl0688.62025MR0994271
30. A. Shapiro, Gateaux, Frechet and Hadamard Directional Differentiability of Functional Solution in Stochastic Programming, Oper. Res. and Statistics Series No. 395, Technion, Haifa, Israel 1989. (1989) 
31. A. Shapiro, On differental stability in stochastic programming, Math. Programming A47 (1990), 107-115. (1990) MR1054844
32. H. White, Maximum likelihood estimation of misspecified models, Econometrica 50 (1982), 1-25. (1982) Zbl0478.62088MR0640163

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