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Note: Normal prediction under linear‐quadratic loss

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  • Michael Cain

Abstract

The prediction of the value of a normal random variable is considered in the presence of combined linear and quadratic loss. It is shown that the optimal prediction is an additive adjustment to the predictive mean, the adjustment being the product of the predictive standard deviation and an appropriate adjustment factor. An extensive table of adjustment factor values is presented, and it is noted that for given loss parameters the adjustment is positive unless the predictive variance is sufficiently large. © 1996 John Wiley & Sons, Inc.

Suggested Citation

  • Michael Cain, 1996. "Note: Normal prediction under linear‐quadratic loss," Naval Research Logistics (NRL), John Wiley & Sons, vol. 43(6), pages 917-927, September.
    • Handle: RePEc:wly:navres:v:43:y:1996:i:6:p:917-927
    DOI: 10.1002/(SICI)1520-6750(199609)43:63.0.CO;2-7
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    References listed on IDEAS

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    1. Michael Cain & Christian Janssen, 1995. "Real estate price prediction under asymmetric loss," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 47(3), pages 401-414, September.
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