Adaptive estimation of a function of a mean vector

Martin Fox

Statistics & Probability Letters, 1997, vol. 33, issue 2, 109-115

Abstract: A sample is taken from some r-dimensional distribution with mean vector [mu] and the value of [theta] = P([mu]) is to be estimated. Here P is a polynomial. An initial sample of size n1 is taken and all components are observed. Assume that, after the initial sample, the remaining sampling budget is C and the cost of each new vector taken is c0 with an additional cost cj if component j is observed. A subset D [not equal to] Ø of {1,h.,r} is selected and a second sample of size n2 is taken in which only those components with index j [set membership, variant] D are observed. It is desired to select D to minimize the MSE of the estimator where the components of are the sample means of observed components. Consider the case P([mu]) = [product operator]j-1r [mu]j. Assume that E([product operator]j=1rXj2)

Keywords: Function; of; mean; vector; Minimize; MSE; Multivariate; Observed; subset; of; components; Second-stage; budget; Two; stage (search for similar items in EconPapers)
Date: 1997
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