Expected Value Estimation Task

An Expected Value Estimation Task is a value estimation task of an expected value.

• • …
• Example(s):
  • Given a binomial stochastic process [math]\displaystyle{ B(n,p) }[/math] (such as a slot machine), with [math]\displaystyle{ n=5 }[/math] events of which [math]\displaystyle{ k=1 }[/math] is a success event, what is the expected value for the success probability [math]\displaystyle{ p }[/math]?

    [math]\displaystyle{ = \frac{k}{n} = \frac{1}{5} }[/math].

  • …
• Counter-Example(s):
  • a Maximum Aposteriori Estimation Task.
• See: Maximum Likelihood Estimation.

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References

2012

• http://www.math.uah.edu/stat/point/Estimators.html
  • QUOTE: … Thus, for an unbiased estimator, the expected value of the estimator is the parameter being estimated, clearly a desirable property. On the other hand, a positively biased estimator overestimates the parameter, on average, while a negatively biased estimator underestimates the parameter on average. …

1996

• (Du et al., 1996) ⇒ Z-P Du., J. Arrillaga, and N. Watson. (1996). “Continuous Harmonic State Estimation of Power Systems.” In: Generation, Transmission and Distribution, IEE Proceedings -, vol. 143, no. 4, pp. 329-336. IET,
  • QUOTE: … A conditional expected value estimation in [4] can be shown to be equivalent to the weighted minimum-quadratic norm estimation, with the weighted matrix being the variance submatrix of unmeasured bus injection currents. …

1993

• (Miller et al., 1993) ⇒ John W. Miller, Rod Goodman, and Padhraic Smyth. (1993). “On Loss Functions Which Minimize to Conditional Expected Values and Posterior Probabilities.” In: IEEE Transactions on Information Theory, 39(4).
  • QUOTE: … the formal definition: where v si p (y). dy. If L (y, $) satisfies this property (cl), we call it “P-admissible,” to indicate that the loss function is admissible for use in probability estimation or expected value estimation. …

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