Ghosh–Pratt identity

Ghosh-Pratt identity

Type	Theorem
Field	Mathematical statistics
Statement	${\displaystyle {\text{E}}_{\theta _{0}}[{\text{vol}}(C(X))]=\int _{\theta \neq \theta _{0}}P_{\theta _{0}}(\theta \in C(X))\,d\theta }$
First stated by	Jayanta Kumar Ghosh John Winsor Pratt
First stated in	1961

In mathematical statistics, the Ghosh-Pratt identity is a theorem that establishes a formal relationship between the expected volume of a confidence set and its probability of false coverage. It is a cornerstone of optimal estimation, as it allows the problem of finding the shortest confidence interval to be framed as a problem of maximizing the power of a statistical test.

The identity was independently discovered and published in 1961 by the Indian statistician Jayanta Kumar Ghosh and the American statistician John Winsor Pratt.