Summary
Consistency and asymptotic normality of the m.l.e. are examined in the non-i.i.d. case when the parameters are constrained. Inequality constraints are considered as an application.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Aitchison, J. and Silvey, S. D. (1958). Maximum likelihood estimation of parameters subject to restraints,Ann. Math. Statist.,29, 813–828.
Brown, B. M. (1971). Martingale central limit theorems,Ann. Math. Statist.,42, 59–66.
Cramér, H. (1946).Mathematical Methods of Statistcs, Princeton University Press.
Crowder, M. J. (1975). Maximum likelihood estimation for dependent observations,J. R. Statist. Soc., B,38, 45–53.
Hudson, D. J. (1969). Least-squares fitting of a polynomial constrained to be either non-negative, non-decreasing or convex,J. R. Statist. Soc., B,31, 113–118.
Moran, P. A. P. (1971). Maximum likelihood estimation in non-standard conditions,Proc. Camb. Phil. Soc.,70, 441–450.
Scott, D. J. (1973). Central limit theorems for martingales and for processes with stationary increments using a Skorokhod representation approach,Adv. Appl. Prob.,5, 119–137.
Silvey, S. D. (1959). The Lagrangian multiplier test,Ann. Math. Statist.,30, 389–407.
Wald, A. (1949). Note on the consistency of the maximum likelihood estimate,Ann. Math. Statist.,20, 595–601.
Author information
Authors and Affiliations
About this article
Cite this article
Crowder, M. On constrained maximum likelihood estimation with non-i.i.d. observations. Ann Inst Stat Math 36, 239–249 (1984). https://doi.org/10.1007/BF02481968
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF02481968