Linear discrepancy and weak discrepancy have been studied as a measure of fairness in giving integer ranks to points of a poset. In linear discrepancy, the points are totally ordered, while in weak discrepancy, ties in rank are permitted. In this paper we study the t-discrepancy of a poset, a hybrid between linear and weak discrepancy, in which at most t points can receive the same rank. Intere...

Celebrated theorems of Roth and Matoušek Spencer together show that the discrepancy arithmetic progressions in first $n$ positive integers is $\Theta (n^{1/4})$ . We study analogous problem $\mathbb {Z}_n$ setting. asymptotically determine logarithm for all integer further up to a constant factor many For example, if $n=p^k$ prime power, then (n^{1/3+r_k/(6k)})$ , where $r_k \in \{0,1,2\}$ rema...

The aim of this paper is to present a framework for asymptotic analysis of likelihood ratio and minimum discrepancy test statistics. First order asymptotics are presented in a general framework under minimal regularity conditions and for not necessarily nested models. In particular, these asymptotics give sufficient and in a sense necessary conditions for asymptotic normality of test statistics...

We study the dispersion of a point set, a notion closely related to the discrepancy. Given a real r ∈ (0, 1) and an integer d ≥ 2, let N(r, d) denote the minimum number of points inside the d-dimensional unit cube [0, 1] such that they intersect every axis-aligned box inside [0, 1] of volume greater than r. We prove an upper bound on N(r, d), matching a lower bound of Aistleitner et al. up to a...

We look at a number of simple, but representative, models of extended electroweak gauge structures, and present the general contributions to aμ from the heavy Z ′ and W′ electroweak gauge bosons. Of the models we have examined, none can explain the observed discrepancy between the current experimental value of aμ and the Standard Model prediction if we require that the gauge fields explain the ...