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THE APPROXIMATE DENSITIES OF SOME QUADRATIC FORMS OF STATIONARY RANDOM VARIABLES
Author(s) -
Abril Juan Carlos
Publication year - 1987
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/j.1467-9892.1987.tb00437.x
Subject(s) - mathematics , toeplitz matrix , identity matrix , quadratic equation , pure mathematics , identity (music) , matrix (chemical analysis) , quadratic form (statistics) , type (biology) , combinatorics , eigenvalues and eigenvectors , geometry , ecology , physics , materials science , quantum mechanics , acoustics , composite material , biology
. First we obtain a convenient way of expressing the determinant of the difference between an identity matrix and some products of Toeplitz matrices. Then, using these results, we show that for a large number of normal processes there exist some quadratic forms whose matrices are of Toeplitz type such that their joint density admits an Edgeworth expansion.