A Further Result on the Relevance of the Dispersion of a Radon–Nikodym Derivative to the Problem of Measuring Association
Syed Mustafa Ali, Samuel David Silvey · Journal of the Royal Statistical Society Series B (Statistical Methodology) · 1965
Summary Let x and y be jointly distributed random variables (not necessarily real-valued) and let φ be the Radon–Nikodym derivative of their joint distribution with respect to the product of their marginal distributions. If x′ and y′ are functions of x and y respectively and φ′ is a corresponding derivative for x′ and y′, then the dispersion of φ, as determined by the product of the marginal distributions of x and y, is not less than that of φ′, this being true in the strongest possible sense.