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On a crossroad of resampling plans: bootstrapping elementary symmetric polynomials
Author(s) -
Van Es A. J.,
Helmers R.,
Hušková M.
Publication year - 2000
Publication title -
statistica neerlandica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.52
H-Index - 39
eISSN - 1467-9574
pISSN - 0039-0402
DOI - 10.1111/1467-9574.00128
Subject(s) - bootstrapping (finance) , mathematics , elementary symmetric polynomial , power sum symmetric polynomial , combinatorics , resampling , degenerate energy levels , order (exchange) , complete homogeneous symmetric polynomial , symmetric polynomial , orthogonal polynomials , physics , mathematical analysis , statistics , difference polynomials , polynomial , gegenbauer polynomials , classical orthogonal polynomials , quantum mechanics , finance , matrix polynomial , economics , econometrics
We investigate the validity of the bootstrap method for the elementary symmetric polynomials S ( k ) n =( n k ) −1 Σ 1≤ i 1 < ... < i k ≤ n X i 1 ... X i k of i.i.d. random variables X 1 , ..., X n . For both fixed and increasing order k , as n→∞ the cases where μ=E X 1 [moe2]0, the nondegenerate case, and where μ=E X 1 =0, the degenerate case, are considered.