Asymptotic properties of nonlinear estimates in stochastic models with finite design space

Statistics and Probability Letters

Volumn 79, Issue 21, 2009, Pages 2307-2313

  Pronzato, Luc ^a  

^a UNIVERSITY OF NICE SOPHIA ANTIPOLIS   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 70349622251     PISSN: 01677152     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.spl.2009.07.025     Document Type: Article

References (14)

1. Caines P. A note on the consistency of maximum likelihood estimates for finite families of stochastic processes. Annals of Statistics 3 2 (1975) 539-546
2. Chow Y. Local convergence of martingales and the law of large numbers. Annals of Mathematics and Statistics 36 (1965) 552-558
3. Christopeit N., and Helmes K. Strong consistency of least squares estimators in linear regression models. Annals of Statistics 8 (1980) 778-788
4. Dragalin V., and Fedorov V. Adaptive designs for dose-finding based on efficacy-toxicity response. Journal of Statistical Planning and Inference 136 (2006) 1800-1823
5. Dvoretzky A. Asymptotic normality for sums of dependent random variables. Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability. Probability Theory vol. II (1972), Univ. California Press, Berkeley, California 513-535
6. Hall P., and Heyde C. Martingale Limit Theory and its Applications (1980), Academic Press, New York
7. Jennrich R. Asymptotic properties of nonlinear least squares estimation. Annals of Mathematics and Statistics 40 (1969) 633-643
8. Lai T. Asymptotic properties of nonlinear least squares estimates in stochastic regression models. Annals of Statistics 22 4 (1994) 1917-1930
9. Lai T., Robbins H., and Wei C. Strong consistency of least squares estimates in multiple regression. Proc. Nat. Acad. Sci. USA 75 7 (1978) 3034-3036
10. Lai T., and Wei C. Least squares estimates in stochastic regression models with applications to identification and control of dynamic systems. Annals of Statistics 10 1 (1982) 154-166
11. Pronzato L. Adaptive optimisation and D-optimum experimental design. Annals of Statistics 28 6 (2000) 1743-1761
12. Pronzato, L., 2009. One-step ahead adaptive D-optimal design on a finite design space is asymptotically optimal. Metrika (in press-a). doi:10.1007/s00184-008-0227-y
13. Pronzato, L., 2009. Penalized optimal designs for dose-finding. Journal of Statistical Planning and Inference (in press-b). doi:10.1016/j.jspi.2009.07.012
14. Wu C. Asymptotic theory of nonlinear least squares estimation. Annals of Statistics 9 3 (1981) 501-513