On a Statistical Problem of E. A. Milne

D. R. Cox, Agnes M. Herzberg


A statistical problem posed by the late E. A. Milne is analysed. Observations are expressed in a simple linear way in terms of unknown parameters, there being more parameters than observations. The parameters are estimated by finding their conditional probability distribution under assumptions, plausible in the particular context, that the parameters are generated by a physical random system with simple properties. The form of the estimates and the precision of estimation is examined, in particular as a function of the relation between the number of parameters and the number of observations. Two continuous versions of the problem, one involving a Brownian motion and one a Poisson process, are discussed.

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