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Adaptive estimation of a function of a mean vector

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  • Fox, Martin

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)

Suggested Citation

  • Fox, Martin, 1997. "Adaptive estimation of a function of a mean vector," Statistics & Probability Letters, Elsevier, vol. 33(2), pages 109-115, April.
    • Handle: RePEc:eee:stapro:v:33:y:1997:i:2:p:109-115
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