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the regression (not residual) degrees of freedom in linear models are "the sum of the sensitivities of the fitted values with respect to the observed response values", [11] i.e. the sum of leverage scores. One way to help to conceptualize this is to consider a simple smoothing matrix like a Gaussian blur, used to mitigate data noise. In ...
In mathematics, especially measure theory, a set function is a function whose domain is a family of subsets of some given set and that (usually) takes its values in the extended real number line {}, which consists of the real numbers and .
A set-valued function, also called a correspondence or set-valued relation, is a mathematical function that maps elements from one set, the domain of the function, to subsets of another set. [ 1 ] [ 2 ] Set-valued functions are used in a variety of mathematical fields, including optimization , control theory and game theory .
A function that indicates membership of an element in a set, taking the value 1 if the element is in the set and 0 otherwise. choice function A function that, given a set of non-empty sets, assigns to each set an element from that set. Fundamental in the formulation of the axiom of choice in set theory. choice negation
The set of all velocities through a given point of space is known as the tangent space, and so df gives a linear function on the tangent space: a differential form. With this interpretation, the differential of f is known as the exterior derivative , and has broad application in differential geometry because the notion of velocities and the ...
The set-theoretic support of , written (), is the set of points in where is non-zero: = {: ()}. The support of f {\displaystyle f} is the smallest subset of X {\displaystyle X} with the property that f {\displaystyle f} is zero on the subset's complement.
This article lists mathematical properties and laws of sets, involving the set-theoretic operations of union, intersection, and complementation and the relations of set equality and set inclusion. It also provides systematic procedures for evaluating expressions, and performing calculations, involving these operations and relations.
A likelihood region is the set of all values of θ whose relative likelihood is greater than or equal to a given threshold. In terms of percentages, a p % likelihood region for θ is defined to be. [ 1 ] [ 3 ] [ 6 ]