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Existence of the Minimum Variance Unbiased Estimator (MVUB)

Module by: Clayton Scott, Robert Nowak

Does an MVUB estimator exist? Suppose there exist three unbiased estimators: θ̂1 θ 1 , θ̂2 θ 2 , and θ̂3 θ 3 . Two possibilities exist, as shown in Figure 1 and Figure 2.

Figure 1
Figure 1 ()
Figure 2: No MVUB estimator exists!
Figure 2 ()

Finding the MVUB Estimator

There is no simple, general procedure for finding the MVUB estimator.

In the next several lectures we will discuss several approaches:

  1. Determine the so-called Cramer-Rao lowerbound (CRLB) and verify that the estimator achieves it.
  2. Apply the Rao-Blackwell theorem (we talked about this earlier in the course).
  3. Further restrict the estimator to a class of estimators (e.g., linear or polynomial functions of the data).

Outline of Remainder of Course

  1. The Cramer-Rao Lower Bound
  2. Linear Statistical Models
  3. Maximum Likelihood Estimation
  4. Bayesian Estimation
  5. Waveform Estimation - Wiener and Kalman Filters
  6. Adaptive Filtering

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