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Random function prediction and Stein's identity

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  • Nicoleris, Theodoros
  • Sagris, Anthony

Abstract

Let X=(X1,X2,...,Xn) be a size n sample of i.i.d. random variables, whose distribution belong to the one-parameter ([theta]) continuous exponential family. We examine prediction functions of the form [theta]mh(X),m[greater-or-equal, slanted]1, where h is a polynomial in X. A natural identity that first appeared in Stein (Stein, 1973) and has been widely exploited since, is discussed in relation to members of such a family. Mild regularity conditions are also introduced that imply the nonexistence of a uniformly minimum mean squared error predictor for these functions.

Suggested Citation

  • Nicoleris, Theodoros & Sagris, Anthony, 2002. "Random function prediction and Stein's identity," Statistics & Probability Letters, Elsevier, vol. 59(3), pages 293-305, October.
    • Handle: RePEc:eee:stapro:v:59:y:2002:i:3:p:293-305
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    References listed on IDEAS

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    1. Arthur Cohen & Harold Sackrowitz, 1990. "Admissibility of estimators of the probability of unobserved outcomes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 42(4), pages 623-636, December.
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    Cited by:

    1. Kumar Kattumannil, Sudheesh, 2009. "On Stein's identity and its applications," Statistics & Probability Letters, Elsevier, vol. 79(12), pages 1444-1449, June.

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