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Is that a unbiased estimator?

  1. Oct 17, 2012 #1
    first of all...what is an unbiased estimator??
    how to check whether a reggression provide an unbiased estimator?

  2. jcsd
  3. Oct 17, 2012 #2

    The following three events can cause biased estimators:

    1) Omitted variable bias.
    2) cov(error,regressors) [itex]\not=[/itex] 0
    3) cov(regressor1, regressor2) [itex]\not=[/itex] 0
    4) Model mis-specification (eg not including a squared term when you should - do a RAMSEY RESET test).
  4. Oct 17, 2012 #3
    An unbiased estimator is a sample function:
    Z_n = f(X_1, \ldots, X_n)
    such that, for an i.i.d. sample with a parameter of the distribution θ that we are trying to estimate, has the property:
    \mathrm{E}\left[Z_n \right] = \theta
    If this does not hold for a finite n, but is true as [itex]n \rightarrow \infty[/itex], then we say that the estimator is asymptotically unbiased.

    In general, if the function f is some non-polynomial function, it is very hard to check the bias of the estimator. If, on the other hand, the estimator is a (symmetric) polynomial of degree p (pth moment), we may use some rules for the expectation values. For example, the mean:
    \bar{X}_n \equiv \frac{1}{n} \, \sum_{k = 1}^{n}{X_k}
    has the property:
    \mathrm{E} \left[\bar{X}_n \right] = \frac{1}{n} \, \sum_{k = 1}^{n}{\mathrm{E} \left[ X_k \right]} = E \left[ X \right]
    is the unbiased estimator of the mathematical expectation of the random variable X.
  5. Oct 17, 2012 #4
    can i say if a regression with very low r^2 it doesnt provide unbiased estimator?
  6. Oct 17, 2012 #5
    can i say if a regression with very low r^2 it doesnt provide unbiased estimator?
  7. Oct 17, 2012 #6

    Ray Vickson

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    Science Advisor
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    No. Bias and r^2 are not really related.

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