Generalized Information Ratio

Ratio of generalized parameters

Let P be a class of graphs. A P-set in a graph G is a vertex subset X such that G(X) ∈ P . We define the P-stability number of a graph G, αP(G), as the maximum cardinality of a P-set in G. AP-dominating set in a graph is a dominatingP-set. Accordingly, the P-domination number of a graph G, γP(G), is the minimum cardinality of a P-dominating set in G. For each r ≥ 1, we define a graph G to be an...

Generalized Likelihood Ratio Statistics

Generalized likelihood ratio tests

Generalized Likelihood Ratio Test for Selecting

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...

Generalized Likelihood Ratio Statistics and Wilks Phenomenon

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...