Abstract
Conditional and unconditional confidence intervals have been compared by Grice, Bain, and Engelhardt (Commun. Statist. B7 (1978), 515–524) in terms of the location-scale model with double-exponential distribution form. Preference was found for the conditional intervals based on mean length and coverage probability for untrue parameters values. These two criteria for a location-scale system are shown to be inappropriate criteria for assessing the conditional versus unconditional approaches to inference. The usual ancillarity concept is also noted to be inappropriate. Support for many conditional analyses, however, is found in a more careful formulation of the statistical model.
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References
Brenner, D. and Fraser, D.A.S. (1979): The identification of distribution form. Department of Statistics, University of Toronto.
Cox, D. R. and Hinkley, D. (1974): Theoretical Statistics, London: Chapman and Hall.
Fick, G. (1976): LSAI: Location-scale analysis implemented, Department of Mathematics and Statistics, University of Calgary.
Fisher, R.A. (1934): Two new properties of maximum likelihood. Proc. R. Soc. A 144, 285–307.
Fraser, D.A.S. (1973): The elusive ancillary, Multivariate Statistical Inference, Ed D.G. Kabe and R.P. Gupta, Amsterdam: North Holland Publishing Co.
Fraser, D.A.S. (1976): Necessary analysis and adaptive inference. Jour. Amer. Statist. Assoc. 71, 99–113.
Fraser, D.A.S. (1979): Inference and Linear Models. London: McGraw-Hill.
Grice, J.V., Bain, L.J., and Engelhardt, M. (1978): Comparison of conditional and unconditional confidence intervals for the double exponential distribution. Commun. Statist. B7, 515–524.
Hinkley, D.V. (1978): Likelihood inference about location and scale parameters. Biometrika, 65, 253–261.
Hinkley, D.V. and Efron, B. (1978): Assessing the accuracy of the maximum likelihood estimator: Observed versus expected information. Biometrika, 65, 457–487.
Welch, B.L. (1939): On confidence limits and sufficiency, with particular reference to parameters of location. Ann. Math. Statist. 10, 58–69.
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Fraser, D.A.S., McDunnough, P. Some remarks on conditional and unconditional inference for location-scale models. Statistische Hefte 21, 224–231 (1980). https://doi.org/10.1007/BF02932616
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DOI: https://doi.org/10.1007/BF02932616