Conditionally unbiased estimator ($E_{\theta }(\hat{\theta }\mid \mathcal{C})=\theta$)

An estimator is conditionally unbiased for a parameter if its expectation, conditional on the specified observation or selection event, equals that parameter. Unconditional unbiasedness does not imply this property after selection. Independent new-stage data and the Rao-Blackwell theorem can provide useful constructions.