17,934 research outputs found
Numerical algorithms for the computation of the Smith normal form of integral matrices,
Numerical algorithms for the computation of the Smith normal form of integral matrices are described. More specifically, the compound matrix method, methods based on elementary row or column operations and methods using modular or p-adic arithmetic are presented. A variety of examples and numerical results are given illustrating the execution of the algorithms
Ordinal Probit Functional Regression Models with Application to Computer-Use Behavior in Rhesus Monkeys
Research in functional regression has made great strides in expanding to
non-Gaussian functional outcomes, however the exploration of ordinal functional
outcomes remains limited. Motivated by a study of computer-use behavior in
rhesus macaques (\emph{Macaca mulatta}), we introduce the Ordinal Probit
Functional Regression Model or OPFRM to perform ordinal function-on-scalar
regression. The OPFRM is flexibly formulated to allow for the choice of
different basis functions including penalized B-splines, wavelets, and
O'Sullivan splines. We demonstrate the operating characteristics of the model
in simulation using a variety of underlying covariance patterns showing the
model performs reasonably well in estimation under multiple basis functions. We
also present and compare two approaches for conducting posterior inference
showing that joint credible intervals tend to out perform point-wise credible.
Finally, in application, we determine demographic factors associated with the
monkeys' computer use over the course of a year and provide a brief analysis of
the findings
Statistical eigen-inference from large Wishart matrices
We consider settings where the observations are drawn from a zero-mean
multivariate (real or complex) normal distribution with the population
covariance matrix having eigenvalues of arbitrary multiplicity. We assume that
the eigenvectors of the population covariance matrix are unknown and focus on
inferential procedures that are based on the sample eigenvalues alone (i.e.,
"eigen-inference"). Results found in the literature establish the asymptotic
normality of the fluctuation in the trace of powers of the sample covariance
matrix. We develop concrete algorithms for analytically computing the limiting
quantities and the covariance of the fluctuations. We exploit the asymptotic
normality of the trace of powers of the sample covariance matrix to develop
eigenvalue-based procedures for testing and estimation. Specifically, we
formulate a simple test of hypotheses for the population eigenvalues and a
technique for estimating the population eigenvalues in settings where the
cumulative distribution function of the (nonrandom) population eigenvalues has
a staircase structure. Monte Carlo simulations are used to demonstrate the
superiority of the proposed methodologies over classical techniques and the
robustness of the proposed techniques in high-dimensional, (relatively) small
sample size settings. The improved performance results from the fact that the
proposed inference procedures are "global" (in a sense that we describe) and
exploit "global" information thereby overcoming the inherent biases that
cripple classical inference procedures which are "local" and rely on "local"
information.Comment: Published in at http://dx.doi.org/10.1214/07-AOS583 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
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