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:

    “To revolt is a natural tendency of life. Even a worm turns against the foot that crushes it. In general, the vitality and relative dignity of an animal can be measured by the intensity of its instinct to revolt.”
    —Mikhail Bakunin (1814–1876)

    “I’ll take fifty percent efficiency to get one hundred percent loyalty.”
    —Samuel Goldwyn (1882–1974)