The geometry of the phosphodiester backbone was analyzed for 7739 dinucleotides from 447 selected crystal structures of naked and complexed DNA. Ten torsion angles of a near-dinucleotide unit have been studied by combining Fourier averaging and clustering. Besides the known variants of the A-, B- and Z-DNA forms, we have also identified combined A + B backbone-deformed conformers, e.g. with α/γ switches, and a few conformers with a syn orientation of bases occurring e.g. in G-quadruplex structures. A plethora of A- and B-like conformers show a close relationship between the A- and B-form double helices. A comparison of the populations of the conformers occurring in naked and complexed DNA has revealed a significant broadening of the DNA conformational space in the complexes, but the conformers still remain within the limits defined by the A- and B- forms. Possible sequence preferences, important for sequence-dependent recognition, have been assessed for the main A and B conformers by means of statistical goodness-of-fit tests. The structural properties of the backbone in quadruplexes, junctions and histone-core particles are discussed in further detail.

Although unbiasedness is a basic property of a good test, many tests on vector parameters or scalar parameters against two-sided alternatives are not finite-sample unbiased. This was already noticed by Sugiura [Ann. Inst. Statist. Math. 17 (1965) 261–263]; he found an alternative against which the Wilcoxon test is not unbiased. The problem is even more serious in multivariate models. When testing the hypothesis against an alternative which fits well with the experiment, it should be verified whether the power of the test under this alternative cannot be smaller than the significance level. Surprisingly, this serious problem is not frequently considered in the literature. The present paper considers the two-sample multivariate testing problem. We construct several rank tests which are finite-sample unbiased against a broad class of location/scale alternatives and are finite-sample distribution-free under the hypothesis and alternatives. Each of them is locally most powerful against a specific alternative of the Lehmann type. Their powers against some alternatives are numerically compared with each other and with other rank and classical tests. The question of affine invariance of two-sample multivariate tests is also discussed.

Modern data collection techniques allow to analyze a very large number of endpoints. In biomedical research, for example, expressions of thousands of genes are commonly measured only on a small number of subjects. In these situations, traditional methods for comparison studies are not applicable. Moreover, the assumption of normal distribution is often questionable for high-dimensional data, and some variables may be at the same time highly correlated with others. Hypothesis tests based on interpoint distances are very appealing for studies involving the comparison of means, because they do not assume data to come from normally distributed populations and comprise tests that are distribution free, unbiased, consistent, and computationally feasible, even if the number of endpoints is much larger than the number of subjects. New tests based on interpoint distances are proposed for multivariate studies involving simultaneous comparison of means and variability, or the whole distribution shapes. The tests are shown to perform well in terms of power, when the endpoints have complex dependence relations, such as in genomic and metabolomic studies. A practical application to a genetic cardiovascular case-control study is discussed.