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Bounds for moments through a general orthogonal expansion in a pre‐hilbert space‐I
Author(s) -
Mathai A. M.
Publication year - 1975
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3315096
Subject(s) - square integrable function , orthonormal basis , hilbert space , mathematics , representation (politics) , integrable system , space (punctuation) , cube (algebra) , product (mathematics) , pure mathematics , unit cube , rigged hilbert space , square (algebra) , orthonormality , orthogonal functions , mathematical analysis , combinatorics , reproducing kernel hilbert space , physics , geometry , computer science , operating system , politics , political science , law , quantum mechanics
Abstract Bounds are obtained for the product moments of an arbitrary finite number of ordered random variables. These bounds are obtained with the help of a representation of an arbitrary function in terms of a complete orthonormal system in a pre‐Hilbert space of square integrable functions defined in a k‐dimensional unit cube.