


Why unbiased, and why inconsistent ...

Can someone explain it in more details?

  • $\begingroup$ What do you already know about the definition of each term? $\endgroup$ – cardinal Mar 12 '12 at 22:30
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    $\begingroup$ I know that unbiased: it means that expected value of parameters obtained from the process is equal to expected value of parameter obtained for the whole population. And that strong consistency means that when number of samples n increases then estimated value almost surely goes to the value of parameter in whole population $\endgroup$ – Darqer Mar 12 '12 at 23:09
  • $\begingroup$ @Darqer:What's unclear? $\endgroup$ – Ashok Mar 13 '12 at 6:00
  • $\begingroup$ I cannot understand how unbiased estimator might be inconsistent. If according to the definition expected value of parameters obtained from the process is equal to expected value of parameter obtained for the whole population how can estimator not converge to parameter in whole population. $\endgroup$ – Darqer Mar 13 '12 at 9:05



  • $\begingroup$ I may ask a trivial Q, but that's what led me to this Q&A here: why is expected value of a known sample still equals to an expected value of the whole population? Intuitively I'd expect expected value of a known sample be equal to itself, e.g. $\mathbb{E}(0) = 0$ $\endgroup$ – Kentzo Oct 9 '18 at 23:59
  • $\begingroup$ @Kentzo Because the sample $\widetilde{x}$ is itself a random variable!! This is very important and is something that I struggled to understand for a long time myself, so I understand your confusion. The best example I could think of is: imagine you are measuring height and are drawing samples (people) at random from the population (humanity). If you know the average height is $\mu = 160$cm, your first sample might be $170$cm, but you still *expect* the average height to be $\mu = 160$, so $\mathbb{E}(\widetilde{x}) = \mu = 160$cm. $\endgroup$ – baibo Jan 1 '20 at 19:12
  • $\begingroup$ Ah, so $\tilde{x} = x_1$ is essentially $\tilde{x} = \tilde{x}$ since $x_1$ can have any value from the population. $\endgroup$ – Kentzo Jan 2 '20 at 20:50



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