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Personal bibliography of
Kenneth Willcox Wachter
[ CalNetDS
- MGP
- MathScinet
]
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Found 2 works with YEAR equal to " 1978"
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Kenneth W. Wachter, E.A. Hammel and P. Laslett
Statistical Studies of Historical Social Structure
Academic Press. New York, NY (1978).
[GScholar?]
[BibTeX]
@book{WACHTER:1978:SSOHSS,
AUTHOR = {Wachter, Kenneth W. and Hammel, E.A. and Laslett, P.},
TITLE = {Statistical Studies of Historical Social Structure},
YEAR = {1978},
ISBN = {0127291504, 9780127291505},
PUBLISHER = {Academic Press},
ADDRESS = {New York, NY},
}
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K.W. Wachter
The strong limits of random matrix spectra for sample matrices of independent elements
Ann. Probab. 6 (No. 1), 1--18 (1978).
[GScholar?]
[ZM] [MR] [DOI]
[BibTeX]
Abstract: This paper proves almost-sure convergence of the empirical measure of the normalized singular values of increasing rectangular submatrices of an infinite random matrix of independent elements. The limit is the limit as both dimensions grow large in some ratio. The matrix elements are required to have uniformly bounded central $2 + \delta$th moments, and the same means and variances within a row. The first section (relaxing the restriction on variances) proves any limit-in-distribution to be a constant measure rather than a random measure, establishes the existence of subsequences convergent in probability, and gives a criterion for almost-sure convergence. The second section proves the almost-sure limit to exist whenever the distribution of the row variances converges. It identifies the limit as a nonrandom probability measure which may be evaluated as a function of the limiting distribution of row variances and the dimension ratio. These asymptotic formulae underlie recently developed methods of probability plotting for principal components and have applications to multiple discriminant ratios and other linear multivariate statistics.
@article{WACHTER:1978:TSLORM:MR0467894,
AUTHOR = {Wachter, K.W.},
TITLE = {The strong limits of random matrix spectra for sample matrices of
independent elements},
JOURNAL = {Ann. Probab.},
ISSN = {0091-1798},
VOLUME = {6},
NUMBER = {1},
YEAR = {1978},
PAGES = {1--18},
MRCLASS = {60F15},
MRREVIEWER = {V. L. Girko},
ZBLCLASS = {60F15;62H25},
ID = {info:zbl/0374.60039, info:mr/MR0467894 (57 \#7744),
info:doi/10.1214/aop/1176995607},
ABSTRACT = {This paper proves almost-sure convergence of the empirical measure
of the normalized singular values of increasing rectangular
submatrices of an infinite random matrix of independent elements.
The limit is the limit as both dimensions grow large in some ratio.
The matrix elements are required to have uniformly bounded central
$2 + \delta$th moments, and the same means and variances within a
row. The first section (relaxing the restriction on variances)
proves any limit-in-distribution to be a constant measure rather
than a random measure, establishes the existence of subsequences
convergent in probability, and gives a criterion for almost-sure
convergence. The second section proves the almost-sure limit to
exist whenever the distribution of the row variances converges. It
identifies the limit as a nonrandom probability measure which may
be evaluated as a function of the limiting distribution of row
variances and the dimension ratio. These asymptotic formulae
underlie recently developed methods of probability plotting for
principal components and have applications to multiple discriminant
ratios and other linear multivariate statistics.},
}
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