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7.4 PROPERTIES OF ESTIMATORS

7.4 PROPERTIES OF ESTIMATORS. 1 properties. Unbiased estimation.  is a nonrandom parameter  is a random parameter. For N observation data:. Commonly, quantities of observation data are beneficial to properties of estimators. Biased estimation:. Neyman Fisher factor theory.

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7.4 PROPERTIES OF ESTIMATORS

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  1. 7.4 PROPERTIES OF ESTIMATORS 1 properties Unbiased estimation  is a nonrandom parameter  is a random parameter For N observation data: Commonly, quantities of observation data are beneficial to properties of estimators. Biased estimation:

  2. Neyman Fisher factor theory effectiveness To unbiased estimation, variance get to least consistent sufficient

  3. Var of unbiased estimation: 2 Cramer-Rao Low Bound (1) nonrandom parameter CRLB

  4. In the condition of： An unbiased estimation，if variance can get to CRLB，is ML estimation,and it’s a best estimation.

  5. Because if It is certain for ML estimation of follow two expressions: so

  6. For example：

  7. unbiased

  8. (2) CRLB of random parameter MSE of unbiased estimation: If MSE get to the least need:

  9. An unbiased estimation，if variance can get to CRLB，is MAP estimation, and MS equal to ML in this condition. example：

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