Abstract
This chapter discusses Cramér–Rao inequality. In its simplest form, the Cramér–Rao inequality asserts that under regularity conditions, the variance of an unbiased estimator of a parametric function is at least the square of the derivative of that function divided by the Fisher information in the sample for all values of the unknown parameter. The Cramér–Rao inequality holds with the information in the sample equal to the information in a single observation times the expected sample size. The Cramér–Rao inequality holds for almost every value of the parameter under the sole condition that information be definable. An a.e. version of the Cramér–Rao inequality can be established for sequential estimators under the condition that the information in a single observation be positive.
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