Search results
Results From The WOW.Com Content Network
The Cramér–Rao bound is stated in this section for several increasingly general cases, beginning with the case in which the parameter is a scalar and its estimator is unbiased. All versions of the bound require certain regularity conditions, which hold for most well-behaved distributions. These conditions are listed later in this section.
The quantum Cramér–Rao bound is the quantum analogue of the classical Cramér–Rao bound. It bounds the achievable precision in parameter estimation with a ...
Among his best-known discoveries are the Cramér–Rao bound and the Rao–Blackwell theorem both related to the quality of estimators. [13] Other areas he worked in include multivariate analysis, estimation theory, and differential geometry. His other contributions include the Fisher–Rao theorem, Rao distance, and orthogonal arrays.
The Cramér–Rao bound [9] [10] states that the inverse of the Fisher information is a lower bound on the variance of any unbiased estimator of θ. Van Trees (1968) and Frieden (2004) provide the following method of deriving the Cramér–Rao bound, a result which describes use of the Fisher information.
In statistics, efficiency is a measure of quality of an estimator, of an experimental design, [1] or of a hypothesis testing procedure. [2] Essentially, a more efficient estimator needs fewer input data or observations than a less efficient one to achieve the Cramér–Rao bound.
The Cramér–Rao bound is a corollary of this result. Proof. Let P and Q be probability distributions (measures) on the real line, whose first moments exist, ...
It is a generalization of the Cramér–Rao bound; compared to the Cramér–Rao bound, it is both tighter and applicable to a wider range of problems. However, it is usually more difficult to compute. The bound was independently discovered by John Hammersley in 1950, [1] and by Douglas Chapman and Herbert Robbins in 1951. [2]
Another influential paper co-authored with his student Harold Silverstone established the lower bound on the variance of an estimator, [6] now known as Cramér–Rao bound. [7] He was elected to the Royal Society of Literature for his World War I memoir, Gallipoli to the Somme. [8]