arXiv subjects

Vered Madar

Publications and source records attributed to Vered Madar.

2 recordsLinked to original sources

arXiv2015

Direct formulation to Cholesky decomposition of a general nonsingular correlation matrix

We present two novel, explicit representations of Cholesky factor of a nonsingular correlation matrix. The first representation uses semi-partial correlation coefficients as its entries. The second, uses an equivalent form of the square roots of the differences between two ratios of successive determinants. Each of the two new forms enjoys parsimony of notations and offers a simpler alternative to both spherical factorization and the multiplicative partial correlation Cholesky matrix (Cooke et al 2011). Two relevant applications are offered for each form: a simple $t$-test for assessing the independence of a single variable in a multivariate normal structure, and a straightforward algorithm for generating random positive-definite correlation matrix. The second representation is also extended to any nonsingular hermitian matrix.

stat.ME↗

arXiv2015

A more practical approach for the Benjamini-Hochberg FDR controlling procedure for huge-scale testing problems

We address a common problem in large-scale data analysis, and especially the field of genetics, the huge-scale testing problem, where millions to billions of hypotheses are tested together creating a computational challenge to perform multiple hypotheses testing procedures. As a solution we propose an alternative algorithm to the well used Linear Step Up procedure of Benjamini and Hochberg (1995). Our algorithm requires linear time and does not require any p-value ordering. It permits separating huge-scale testing problems arbitrarily into computationally feasible sets or chunks. Results from the chunks are combined by our algorithm to produce the same results as the controlling procedure on the entire set of tests, thus controlling the global false discovery rate even when p-values are arbitrarily divided. The practical memory usage may also be determined arbitrarily by the size of available memory.

stat.ME↗