A note on testing two-dimensional normal mean

Summary For the problem of testing a composite hypothesis with one-sided alternatives of the mean vector of a two-dimensional normal distribution, a characterization of similar tests is presented and an unbiased test dominating the likelihood ratio test is proposed. A sufficient condition for admissibility is given, which implies the result given by Cohen et al. (1983,Studies in Econometrics, Time Series and Multivariate Statistics, Academic Press): the admissibility of the likelihood ratio test.     

A generalization of the growth curve model which allows missing data

This study presents methods for estimating and testing hypotheses about linear functions of the unknown parameters in a generalization of the growth curve model which allows missing data. The estimators proposed are best asymptotically normal (BAN). A testing method for large samples is described which uses a test criterion given in general form by Wald. The asymptotic null distribution of the test statistic is a central chi-square variable. A BAN estimator of a linear vector function of the unknown parameters of the expectation model and consistent estimators of the variance-covariance parameters are required for computation.     

The high temperature transition of polyethylene into a Condis phase,described on the basis of the cluster-entropy hypothesis (CEH)

On the basis of atomistic calculations a rotator model of the high temperature Condis phase of polyethylene is proposed. Its cooperative statistical treatment (using CEH for the lateral packing of chains) explains the first order transition from the all-trans crystal as well as the transition dataT _t ,S _t ,V _t . We found that the normal melting (i. e. at pressures below the triple point) is also governed by the onset of the Condis phase.This abbreviation was introduced by B. Wunderlich [1], to describe conformationally disordered oligomer or polymer crystals.Dedicated to Professor Dr. R. Kosfeld on the occasion of his 60th birthday.     

The Split of the Dirac Hamiltonian into Precisely Predictable Energy Components

We are dealing with the Dirac Hamiltonian H = H₀ + V with no magnetic field and radially symmetric electrostatic potential V = V(r), preferably the Coulomb potential. While the observable H is precisely predictable, its components H₀ (relativistic mass) and V (potential energy) are not. However they both possess precisely predictable approximations H₀ and V which approximate accurately if the particle is not near its nucleus. On the other hand, near 0, H₀ and V are practically unpredictable, perhaps in agreement with the fact, that a neutrino also should be in the game. [We have not yet studied the corresponding observables for the ( 12-dimensional) problem of electro-weak interaction.] Mathematically we are focusing on the spectral theory of the unbounded self-adjoint operators H₀ and V . We can prove that V is unitarily equivalent to V(r) again, by a unitary map given as Wiener-Hopf-type singular integral operator in the standard separation of variables for radially symmetric Dirac Hamiltonians. [This is, as far as the continuous spectrum is concerned.] Very similar unitary equivalence holds for H ₀ and H ₀. We are tempted to regard this as a form of renormalization.     

Numerical calculation of the density of prime numbers with a given least primitive root

In this paper the densities of prime numbers having the least primitive root , where is equal to one of the initial positive integers less than 32, have been numerically calculated. The computations were carried out under the assumption of the Generalised Riemann Hypothesis. The results of these computations were compared with the results of numerical frequency estimations.

     

On the least prime primitive root modulo a prime

We derive a conditional formula for the natural density of prime numbers having its least prime primitive root equal to , and compare theoretical results with the numerical evidence.

     

观测来自银道面的TeV γ射线

给出来自银经79.3866°的银道面的TeV γ射线的观测结果.数据是在1995年10月至1998年11月间的晴朗无月夜,用兴隆站的大气契伦科夫望远镜ACT2和ACT3以向源–背景(ON–OFF)观测方式取得的,总观测时间为224.4h.在望远镜计数服从高斯分布的情况下,导出了最大似然比λ的表达式,它直接给出显著性水平的概率.用它分析观测资料,在统计误差范围内没发现有来自银道面的TeV γ射线.     

双参数指数分布位置参数的统计推断

通过次序统计量 ,得到了双参数指数分布 E(μ,λ)中位置参数μ的一致最小方差无偏估计为nn-1 T(1) -1n-1 T,推导出了 ( T-μ) / ( T-T(1) )的分布与参数μ,λ无关 ,从而得到了μ的置信区间与检验统计量 .     

组合预测的权估计及其显著性检验

提出了组合预测权系数的另一种算法,即从统计角度给出了权重的LS估计及其假设检验,旨在提高预测的精度。