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Just a note

To see how partial estimates work, we need an estimator. For example, because is an unbiased estimator of μY we would expect there to be no mean difference between estimates based upon 3 and 4 values. In other words, we would expect that Σ[ - -j] / n = 0 and E() = E-j

Given that = , if we have ( n = ) four observations, 1.1, 2.2, 3.3 and 4.4, then = (1.1+2.2+3.3+4.4) / 4 = 2.75

Given that -j is calculated without the jth observation, omitting each observation in turn, the four partial estimates of this statistic are:

  1. -1 = (1.1+2.2+3.3+4.4) / 3 = 3.3
  2. -2 = (1.1+2.2+3.3+4.4) / 3 = 2.933
  3. -3 = (1.1+2.2+3.3+4.4) / 3 = 2.567
  4. -4 = (1.1+2.2+3.3+4.4) / 3 = 2.2

The mean of these partial estimates is, as you would expect, 2.75