For 10 points, name this inequality that states that the variance of an unbiased estimator is at least as high as the inverse of the Fisher information, named for two statisticians.
An improvement on this result contains a denominator equal to the chi-square divergence of the probability density function of theta plus delta with respect to the pdf of theta; that improvement is named for Robbins, Chapman, and Hammersley. The single-parameter version of this result can be proven by taking the covariance of a test statistic with the score, using the chain rule, then applying the Cauchy-Schwartz inequality. This result can be used to prove that the maximum likelihood estimator is asymptotically (*) unbiased. Applying this result to a multivariate normal distribution gives a result of sigma-squared over N, and this statement can be used to find the unbiased estimator with the lowest mean-squared error. For 10 points, name this inequality that states that the variance of an unbiased estimator is at least as high as the inverse of the Fisher information, named for two statisticians.
An improvement on this result contains a denominator equal to the chi-square divergence of the probability density function of theta plus delta with respect to the pdf of theta; that improvement is named for Robbins, Chapman, and Hammersley.
Cramer-Rao bound [or the information inequality]