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Biometrika 1977 64(1):51-57; doi:10.1093/biomet/64.1.51
© 1977 by Biometrika Trust
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Optimal use of extraneous information concerning a nuisance parameter

DENIS HEMON

Unité de Recherches Statistiques, Institut National de la Santé et de la Recherche Médicale Villejuif, France

Suppose that N experiments can be carried out. One type of experiment provides observations, Y, depending on {alpha}, the parameter of interest and ß a nuisance parameter. The other type provides observations, Z, depending on ß and {gamma}. How should the N experiments be divided between the two types to estimate {alpha} optimally? The existence and uniqueness of an optimal allocation is proved and a method of calculation is provided. In the particular case of ß being scalar, the optimal allocation is given explicitly, and is not necessarily the simple solution consisting of performing only experiments of the first type. In this case, an observation Z may provide additional information concerning {alpha} which is more useful than a further observation Y. An application to estimation from truncated data is described and further generalizations are considered.

Key Words: Nonlinear design • Nuisance parameter • Optimal experiment • Truncated data


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