منابع مشابه
Lognormal scale invariant random measures
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In this article, we consider the continuous analog of the celebrated Mandelbrot star equation with infinitely divisible weights. Mandelbrot introduced this equation to characterize the law of multiplicative cascades. We show existence and uniqueness of measures satisfying the aforementioned continuous equation. We obtain an explicit characterization of the structure of these measures, which ref...
متن کاملScale Invariant Conditional Dependence Measures
In this paper we develop new dependence and conditional dependence measures and provide their estimators. An attractive property of these measures and estimators is that they are invariant to any monotone increasing transformations of the random variables, which is important in many applications including feature selection. Under certain conditions we show the consistency of these estimators, d...
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We characterize measures of school segregation for any number of ethnic groups using a set of purely ordinal axioms that includes Scale Invariance: a school districts segregation ranking should be invariant to changes that do not a¤ect the distribution of ethnic groups across schools. The symmetric Atkinson index is the unique such measure that treats ethnic groups symmetrically and that ranks...
متن کاملScale Invariant Conditional Dependence Measures
Proof. We will prove the general case of conditional dependence measure since the other case follows trivially as a special case when Z = ∅. The kernel-free property of the dependence measures is used to prove the result. The proof essentially uses change of variables formulas for transformation of random variables. From Theorem 1, we have
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ژورنال
عنوان ژورنال: Probability Theory and Related Fields
سال: 2012
ISSN: 0178-8051,1432-2064
DOI: 10.1007/s00440-012-0412-9