论文信息 - On the sampling interpretation of confidence intervals and hypothesis tests in the context of conditional maximum likelihood estimation

On the sampling interpretation of confidence intervals and hypothesis tests in the context of conditional maximum likelihood estimation

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.

E. Maris

[1] A. Gardner. Methods of Statistics , 1941 .

[2] E. L. Lehmann,et al. Theory of point estimation , 1950 .

[3] J. Kiefer,et al. CONSISTENCY OF THE MAXIMUM LIKELIHOOD ESTIMATOR IN THE PRESENCE OF INFINITELY MANY INCIDENTAL PARAMETERS , 1956 .

[4] E. B. Andersen,et al. Asymptotic Properties of Conditional Maximum‐Likelihood Estimators , 1970 .

[5] Erling B. Andersen,et al. Conditional Inference and Models for Measuring , 1974 .

[6] Franklin A. Graybill,et al. Theory and Application of the Linear Model , 1976 .

[7] E. B. Andersen,et al. Estimating the parameters of the latent population distribution , 1977 .

[8] Gerhard H. Fischer,et al. On the existence and uniqueness of maximum-likelihood estimates in the Rasch model , 1981 .

[9] Norman Verhelst,et al. Maximum Likelihood Estimation in Generalized Rasch Models , 1986 .

[10] Dean Follmann,et al. Consistent estimation in the rasch model based on nonparametric margins , 1988 .

[11] Cees A. W. Glas,et al. The derivation of some tests for the rasch model from the multinomial distribution , 1988 .

[12] B. Lindsay,et al. Semiparametric Estimation in the Rasch Model and Related Exponential Response Models, Including a Simple Latent Class Model for Item Analysis , 1991 .

[13] J. Pfanzagl. A case of asymptotic equivalence between conditional and marginal maximum likelihood estimators , 1993 .

[14] J. Pfanzagl. On Item Parameter Estimation in Certain Latent Trait Models , 1994 .