The least favorable noise

The Structure of Least-Favorable Noise in Gaussian Vector Broadcast Channels

The sum capacity of the Gaussian vector broadcast channel is the saddle point of a Gaussian mutual information game in which the transmitter maximizes the mutual information by choosing the best transmit covariance matrix subject to a power constraint, and the receiver minimizes the mutual information by choosing a least-favorable noise covariance matrix subject to a diagonal constraint. This r...

On Least Favorable Set Fui~ctions

Gaussian Assumption: the Least Favorable but the Most Useful

Gaussian assumption is the most well-known and widely used distribution in many fields such as engineering, statistics and physics. One of the major reasons why the Gaussian distribution has become so prominent is because of the Central Limit Theorem (CLT) and the fact that the distribution of noise in numerous engineering systems is well captured by the Gaussian distribution. Moreover, feature...

On least favorable configurations for step-up-down tests

This paper investigates an open issue related to false discovery rate (FDR) control of step-up-down (SUD) multiple testing procedures. It has been established in earlier literature that for this type of procedure, under some broad conditions, and in an asymptotical sense, the FDR is maximum when the signal strength under the alternative is maximum. In other words, so-called “Dirac uniform confi...

Jeffreys ’ prior is asymptotically least favorable under entropy risk

We provide a rigorous proof that Jeffreys’ prior asymptotically maximizes Shannon’s mutual information between a sample of size n and the parameter. This was conjectured by Bernard0 (1979) and, despite the absence of a proof, forms the basis of the reference prior method in Bayesian statistical analysis. Our proof rests on an examination of large sample decision theoretic properties associated ...