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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
More From: Recent Advances in Statistics: Papers in Honor of Herman Chernoff on His Sixtieth Birthday
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.