Information Theoretic Parameter Estimation
Information theory is closely associated with the estimation theory. For example, the maximum entropy (MaxEnt) principle has been widely used to deal with estimation problems given incomplete knowledge or data. Another example is the Fisher information, which is a central concept in statistical estimation theory. Its inverse yields a fundamental lower bound on the variance of any unbiased estimator, i.e., the well-known Cramer–Rao lower bound (CRLB). An interesting link between information theory and estimation theory was also shown for the Gaussian channel, which relates the derivative of the mutual information with the minimum mean square error (MMSE) .