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Fisher Information and Cramér-Rao Lower Bound
| Content Provider | Scilit |
|---|---|
| Author | Ober, Raimund J. Ward, E. Sally Chao, Jerry |
| Copyright Year | 2020 |
| Description | In the prior chapter, we have considered parameter estimation problems such as the determination of the mean of a random variable and the localization of an object. We have also discussed approaches to solving such estimation problems, and in particular, the maximum likelihood estimator. Furthermore, for assessing the quality of an estimation approach, we have introduced the notion of the bias and the variance of an estimator. Here, it is the variance or standard deviation of an estimator that we consider in more detail. Provided that an estimator is not biased, we would want to use an estimator with the smallest variance in order to have a small “spread” of the estimates in the case of repeat estimates. Importantly, the variance of an unbiased estimator cannot be arbitrarily small. There is a bound, the Cramér-Rao lower bound, that provides a lower limit for the variance of an unbiased estimator. The Cramér-Rao lower bound, which is the inverse of a quantity known as the Fisher information matrix, is the subject of this chapter. Besides providing a benchmark against which the performance of an estimator can be assessed, we will demonstrate in later chapters that the Cramér-Rao lower bound is a useful tool for experimental design. Book Name: Quantitative Bioimaging |
| Related Links | https://content.taylorfrancis.com/books/download?dac=C2018-0-82936-1&isbn=9780429469893&doi=10.1201/9780429469893-21&format=pdf |
| Ending Page | 330 |
| Page Count | 18 |
| Starting Page | 313 |
| DOI | 10.1201/9780429469893-21 |
| Language | English |
| Publisher | Informa UK Limited |
| Publisher Date | 2020-11-27 |
| Access Restriction | Open |
| Subject Keyword | Book Name: Quantitative Bioimaging Statistics and Probability Fisher Chapter Unbiased Rao Lower Bound Cramér Rao Lower |
| Content Type | Text |
| Resource Type | Chapter |
