Abstract
With a parametric model, a measure of departure for an interest parameter is often easily constructed but frequently depends in distribution on nuisance parameters; the elimination of such nuisance parameter effects is a central problem of statistical inference. Fraser & Wong (1993) proposed a nuisance-averaging or approximate Studentization method for eliminating the nuisance parameter effects. They showed that, for many standard problems where an exact answer is available, the averaging method reproduces the exact answer. Also they showed that, if the exact answer is unavailable, as say in the gamma-mean problem, the averaging method provides a simple approximation which is very close to that obtained from third order asymptotic theory. The general asymptotic accuracy, however, of the method has not been examined. In this paper, we show in a general asymptotic context that the averaging method is asymptotically a second order procedure for eliminating the effects of nuisance parameters.
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Abebe, F., Cakmak, S., Cheah, P.K., Fraser, D.A.S., Kuhn, J., Reid, N., and Tapia, A. (1992). Third order asymptotic model: exponential and location type approximations.Parisankhyan Samikka 1, 1–5.
Barndorff-Nielsen O.E. (1991). Modified signed log likelihood ratio.Biometrika 78, 557–564.
Cox, D.R. (1975). A note on partially Bayes inference and linear models.Biometrika 62, 651–654.
DiCiccio, T., Field, C., and Fraser, D.A.S. (1990). Approximation of marginal tail probabilities and inference for scalar parameters.Biometrika 77, 77–95.
Fisher, R.A. (1934). Two new properties of mathematical likelihood.Proc. Royal Soc. A 144, 285–307.
Fraser, D.A.S., and Reid (1993). Simple asymptotic connections between densities and cumulant generating function leading to accurate approximations for distribution functions.Statist. Sinica. 3, 67–82.
Fraser, D.A.S., and Reid (1995). Ancillaries and third order significance.Utilitas Mathematica 47, 33–53.
Fraser, D.A.S., and Wong, A. (1993). Approximation Studentization with marginal and conditional inference.Canad. J. Statist. 21, 313–320.
Kalbfleisch, J.D., and Sprott, D. (1973). Marginal and conditional likelihood.Sankyhā A 35, 311–328.
Shuie, W.K. and Bain, L.J. (1983). A two-sample test of equal gamma distribution scale parameters with unknown common shape parameter.Technometrics 25, 377–381.
Student (1908). The probable error of a mean.Biometrika 6, 1–25.
Wong, A. (1995). On approximate inference for the two-parameter gamma model.Statist. Papers 36, 49–59.
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Fraser, D.A.S., Wong, A.C.M. On the accuracy of approximate studentization. Statistical Papers 38, 351–356 (1997). https://doi.org/10.1007/BF02925274
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DOI: https://doi.org/10.1007/BF02925274