On the sampling interpretation of confidence intervals and hypothesis tests in the context of conditional maximum likelihood estimation
- E. Maris
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In the context ofconditional maximum likelihood (CML) estimation, confidence intervals can be interpreted in three different ways, depending on the sampling distribution under which these confidence intervals contain the true parameter value with a certain probability. These sampling distributions are (a) the distribution of the data given theincidental parameters, (b) the marginal distribution of the data (i.e., with the incidental parameters integrated out), and (c) the conditional distribution of the data given the sufficient statistics for the incidental parameters. Results on the asymptotic distribution of CML estimates under sampling scheme (c) can be used to construct asymptotic confidence intervals using only the CML estimates. This is not possible for the results on the asymptotic distribution under sampling schemes (a) and (b). However, it is shown that theconditional asymptotic confidence intervals are also valid under the other two sampling schemes.
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- On the sampling interpretation of confidence intervals and hypothesis tests in the context of conditional maximum likelihood estimation
Volume 63, Issue 1 , pp 65-71
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- CML estimation
- confidence intervals
- conditional inference
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- E. Maris (1) (2)
- Author Affiliations
- 1. Department of Mathematical Psychology (NICI), Catholic University of Nijmegen, P.O. Box 9104, 6500 HE, Nijmegen, The Netherlands
- 2. National Institute for Educational Measurement (CITO), The Netherlands