Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-26T00:25:58.787Z Has data issue: false hasContentIssue false
  • English
  • Français

Maximum-likelihood estimators with known incidental parameters

Published online by Cambridge University Press:  24 October 2008

P. A. P. Moran
P. A. P. Moran
Affiliation:
The Australian National University, Canberra
Get access Rights & Permissions [Opens in a new window]

Extract

Suppose we have a sample of N independent random variables X1, …, XN where Xi has the distribution F(X|θ, øi). θ is a k-dimensional ‘structural’ parameter (θ(1), …, θ(k)), and the øi are scalar or vector ‘incidental’ parameters in some given space. The Xi may be scalar or vector random variables which are either discrete in which case we write f(X|θ, øi) for the probability associated with a given point, or else continuous random variables with a probability density f(X|θ, øi). In either case we sup pose the support of the probability distribution to be fixed. We aim to estimate the true value of θ by maximum-likelihood methods.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 72 , Issue 2 , September 1972 , pp. 233 - 241
Copyright
Copyright © Cambridge Philosophical Society 1972

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Jenrich, R. I.Asymptotic properties of non-linear least squares regression. Ann. Math. Statist. 40 (1969), 633–643.Google Scholar
(2)Kalbfleisch, J. D. and Sprott, D. A.Application of likelihood methods to models involving large numbers of parameters. J. Roy. Statist. Soc. B 32 (1970), 175–208.Google Scholar
(3)Kiefer, J. and Wolfowitz, J.Consistency of the maximum likelihood estimator in the presence of infinitely many incidental parameters. Ann. Math. Statist. 27 (1956), 887–906.CrossRefGoogle Scholar
(4)Malinvaud, E.The consistency of non-linear regressions. Ann. Math. Statist. 41 (1970), 956–969.Google Scholar
(5)Moran, P. A. P.The uniform consistency of maximum likelihood estimators. Proc. Cambridge Philos. Soc. 70 (1971).Google Scholar
(6)Neyman, J. and Scott, E.Consistent estimates based on partially consistent observations. Econometrica 16 (1948), 1–32.Google Scholar
(7)Wald, A.Note on the consistency of the maximum likelihood estimate. Ann. Math. Statist. 20 (1949), 595–601.CrossRefGoogle Scholar
(8)Walker, A. M.On the estimation of a harmonic component in a time series with stationary independent residuals. Biometrika 58 (1971), 21–36.Google Scholar