Efficient Estimator - Relative Efficiency

Relative Efficiency

If and are estimators for the parameter, then is said to dominate if:

  1. its mean squared error (MSE) is smaller for at least some value of
  2. the MSE does not exceed that of for any value of θ.

Formally, dominates if


\mathrm{E}
\left[ (T_1 - \theta)^2
\right]
\leq
\mathrm{E}
\left[ (T_2-\theta)^2
\right]

holds for all, with strict inequality holding somewhere.

The relative efficiency is defined as


e(T_1,T_2)
=
\frac {\mathrm{E} \left} {\mathrm{E} \left}

Although is in general a function of, in many cases the dependence drops out; if this is so, being greater than one would indicate that is preferable, whatever the true value of .

Read more about this topic:  Efficient Estimator

Famous quotes containing the words relative and/or efficiency:

    She went in there to muse on being rid
    Of relative beneath the coffin lid.
    No one was by. She stuck her tongue out; slid.
    Gwendolyn Brooks (b. 1917)

    “Never hug and kiss your children! Mother love may make your children’s infancy unhappy and prevent them from pursuing a career or getting married!” That’s total hogwash, of course. But it shows on extreme example of what state-of-the-art “scientific” parenting was supposed to be in early twentieth-century America. After all, that was the heyday of efficiency experts, time-and-motion studies, and the like.
    Lawrence Kutner (20th century)