For the purpose of testing the spherical uniformity based on i.i.d. directional data (unit vectors) zi, i = 1, . . . , n, Anderson and Stephens (1972) proposed testing procedures based on the statistics Smax = maxu S(u) and Smin = minu S(u), where u is a unit vector and nS(u) is the sum of square of u′zi’s. In this paper we also consider another test statistic Srange = Smax − Smin. We provide f...

this study was designed to elucidate the effect of ascorbic acid on salivary total antioxidant capacity in smokers. in this single blind crossover clinical trial, the whole unstimulated saliva of 30 smokers, who were randomly divided into two groups, was collected. in the first phase after the saliva collection, one group of patients took 500 mg of vitamin c powder, for 3 weeks. then, saliva of...

Identifying replicable genetic variants for addiction has been extremely challenging. Besides the common difficulties with genome-wide association studies (GWAS), environmental factors are known to be critical to addiction, and comorbidity is widely observed. Despite the importance of environmental factors and comorbidity for addiction study, few GWAS analyses adequately considered them due to ...

It is the goal of this paper to extend the Empirical Risk Minimization (ERM) paradigm, from a practical perspective, to the situation where a natural estimate of the risk is of the form of a K-sample U -statistics, as it is the case in the K-partite ranking problem for instance. Indeed, the numerical computation of the empirical risk is hardly feasible if not infeasible, even for moderate sampl...

[1] The generation of a posteriori distribution of a statistic of propagation loss conditioned on observed radar sea clutter is described. The statistic u is the 20th percentile level of the two-way propagation loss at a 5-m height over the 10–60 km range interval. A discrete implementation of the Bayesian paradigm is employed. The forward mapping from the space of environmental parameters into...

Hatayama et al. conjectured fermionic formulas associated with tensor products of U ′ q (g)-crystals B. The crystals B correspond to the Kirillov–Reshetikhin modules which are certain finite dimensional U ′ q (g)-modules. In this paper we present a combinatorial description of the affine crystals Br,1 of type D n . A statistic preserving bijection between crystal paths for these crystals and ri...

For t ≥ 0, let X(t) = (X0(t), . . . , Xp(t)) , where Xi(t) denotes the integral of the ith order Legendre polyonimal with respect to the same Brownian motion described by the corresponding standard deviation (0 ≤ i ≤ p). We obtain the exact tail behavior of P ( sup0≤t≤h |X(t)| > u ) as u → ∞, and the limit distribution of sup0≤t≤T |X(t)| as T → ∞. These processes naturally arise in the context ...

Han’s maximum rank correlation (MRC) estimator is shown to be √ n-consistent and asymptotically normal. The proof rests on a general method for determining the asymptotic distribution of a maximization estimator, a simple U-statistic decomposition, and a uniform bound for degenerate U-processes. A consistent estimator of the asymptotic covariance matrix is provided, along with a result giving t...

In this paper, we study the distribution of so-called “Yule’s nonsense correlation statistic” on a time interval [0,T] for horizon T>0, when T is large, pair (X1,X2) independent Ornstein-Uhlenbeck processes. This statistic by definition equal to: ρ(T):=Y12(T) Y11(T) Y22(T), where random variables Yij(T), i,j=1,2 are defined as Yij(T):= ∫0TX i(u)Xj(u)du−TX¯iXj¯, X¯i:=1 T∫0TX i(u)du. We assume X1...

We present a novel approach to test for heteroscedasticity of nonstationary time series that is based on Gini’s mean difference logarithmic local sample variances. In order analyse the large behaviour our statistic, we establish new limit theorems U-statistics dependent triangular arrays. derive asymptotic distribution statistic under null hypothesis constant variance and show consistent agains...