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December, 1960 Random Allocation Designs I: On General Classes of Estimation Methods
A. P. Dempster
Ann. Math. Statist. 31(4): 885-905 (December, 1960). DOI: 10.1214/aoms/1177705665


Certain linear estimation procedures for randomized experimental designs are evaluated relative to the criteria of bias, variance and mean square error. For the designs considered, treatment combinations are randomly allocated to experimental units, the randomness being subject only to a wide symmetry condition. Statistical properties refer to the discrete probabilities induced by the randomization hypothesis. Section 2 defines the basic statistical model and discusses the question of conditional inference relative to this model. Certain vectorial notation and terminology is introduced in Section 3. Although the theory of the paper applies directly to $k$-factor designs with general $k,$ the notation is set up in Section 3 for a three factor design, and the three factor notation is used throughout, except for Section 5 which discusses an even simpler example. Two general classes of linear unbiased estimators are defined in Section 4 and illustrated in Section 5. In Section 6 it is shown that estimators of the types defined in Section 4 have optimum properties in a wide class of linear estimators. Finally, the theory for the basic model is generalized in Section 7 to cover the case of observations with error. Formal proofs of stated theorems are to be found at the ends of Sections 4.2, 4.3 and 6.


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A. P. Dempster. "Random Allocation Designs I: On General Classes of Estimation Methods." Ann. Math. Statist. 31 (4) 885 - 905, December, 1960.


Published: December, 1960
First available in Project Euclid: 27 April 2007

zbMATH: 0114.10803
MathSciNet: MR125712
Digital Object Identifier: 10.1214/aoms/1177705665

Rights: Copyright © 1960 Institute of Mathematical Statistics

Vol.31 • No. 4 • December, 1960
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