92994378
A note on discriminantal arrangements
Let v O be a fixed affine arrangement of n hyperplanes in general position in Kk . Let U(n, k) denote the set of general position arrangements whose elements are parallel translates of the hyperplanes of v o . Then U(n, k) is the complement of a central arrangement R (n, k). These are the well-known discriminantal arrangements introduced by Y. I. Manin and V. V. Schechtman. In this note we give an explicit description of R (n, k) in terms of the original arrangement v o . In terms of the underlying matroids, _q (n, k) realizes an adjoint of the dual of the matroid associated with v o . Using this description we show that, contrary to the conventional wisdom, neither the intersection lattice of S7 (n, k) nor the topology of U(n, k) is independent of the original arrangement v o .
14391043
Arrangements and cohomology
To a matroidM is associated a graded commutative algebraA=A(M), the Orlik-Solomon algebra ofM. Motivated by its role in the construction of generalized hypergeometric functions, we study the cohomologyH* (A, dω) ofA(M) with coboundary mapdω given by multiplication by a fixed element ω ofA1. Using a description of decomposable relations inA, we construct new examples of “resonant” values of ω, and give a precise calculation ofH1 (A, dω) as a function of ω. We describe the setR1(A={ω|H1(A(M,dω)≠}, and use it as a tool in the classification of Orlik-Solomon algebras, with applications to the topology of complex hyperplane complements. We show thatR1(A) is a complete invariant of the quadratic closure ofA, and show under various hypotheses that one can reconstruct the matroidM, or at least its Tutte polynomial, from the varietyR1(A). We demonstrate with several examples thatR1 is easily calculable, may contain nonlocal components, and that combinatorial properties ofR1(A) are often sufficient to distinguish nonisomorphic rank three Orlik-Solomon algebras.
120219973
Weak convergence of the maximum error of the bootstrap quantile estimate
Weak convergence is established for the maximum deviation of the bootstrap estimate of the sample q-quantile distribution.
122219271
Relative Deficiency of Kernel Type Estimators of Quantiles
Offshore apparatus is disclosed which includes a base, a tower pivotally connected to the base, at least one support member attached to the tower and adapted to slidably support a conductor pipe, and at least one conductor pipe adjacent and substantially parallel to the longitudinal axis of the tower and laterally supported by at least one support member. An articulatable means connects the apparatus to a span of the conductor pipe situated in close proximity to the pivotal connection. This means provides sufficient lateral support to the pipe span to prevent buckling and at the same time controls the configuration of the pipe span as the tower sways to prevent bending stress within the pipe span from attaining a level that will cause the pipe to fail.
120645444
Asymptotic Normality of the Kernel Quantile Estimator
117601894
Best Attainable Rate of Joint Convergence of Extremes
Suppose that the underlying distribution function is ultimately continuous and strictly increasing. In this case the rate of joint convergence of the k largest order statistics, equally standardized, in a sample of n i.i.d. random variables is O(k/n), uniformly in k if, and only if, the underlying distribution function is ultimately a generalized Pareto distribution. Thus, generalized Pareto distributions yield the best rate of joint convergence of extremes.
120399973
Some Best Parameter Estimates for Distributions with Finite Endpoint
Consider n observations on, ,generated independently by a distribution function F which is only partially specified: We require that F has in its upper tail a density f such that as x tends to the right endpoint θ of F. The parameters of interest are a > 0 and b, . Based on the largest order statistics in the sample, we can define in case α > 1 /2 estimates of α, b and θ that behave asymptotically like the BLUE of θ as if α was known and like the UMVU estimates of and θin some ideal model as if θ was known. We show in addition that the BLUE estimate of θ can be outperformed by a bias corrected largest order statistic.