A generalized likelihood ratio test is considered for testing acoustic propagation models in the context of environmental parameter inversion. In the following, we use the term \hierarchy of models" to denote a sequence of model structures M1;M2;... in which each particular model structure Mn contains all previous ones as special cases. We propose a combined parameter estimation and multiple se...

The likelihood ratio theory contributes tremendous success to parametric inferences. Yet, there is no general applicable approach for nonparametric inferences based on function estimation. Maximum likelihood ratio test statistics in general may not exist in nonparametric function estimation setting. Even if they exist, they are hard to find and can not be optimal as shown in this paper. We intr...

In many real world problems, it is difficult to precisely specify probability distributions. Our models for data may involve unknown parameters or other characteristics. Here are a few motivating examples. Example: Unknown amplitudes/delays in wireless communications. We don't always know how many relays a signal will go through, how strong the signal will be at each receiver, the distance betw...