Interval estimation of the critical value in a general linear model

Summary This paper concerns interval estimation of the critical value θ which satisfies under the general linear model,Y _i =μ(x _i )+ε _i (i=1,2,···), where for and the functional forms off _j ^′ s are known. From an asymptotic expansion it is shown that, under reasonable conditions, the limiting distribution of is normal. Thus in the large-sample case a confidence interval for θ can be obtained. Such a result is useful when one is interested in carrying out a retrospective analysis rather than designing the experiment (as in the Kiefer-Wolfowitz procedure). In Section 3 a sequential procedure is considered for confidence intervals with fixed width 2d. It is shown that, for a given stopping variableN, is also asymptotically normal asd→0. Thus the coverage probability converges to 1−α (preassigned) asd→0. An example of application in estimating the phase parameter in circadian rhythms is given for the purpose of illustration. Research partially supported by the NSF Grant DMS-8502346.     

Analysis of long-term distributions of calibration parameters and calibration intervals for an atomic absorption spectrophotometer

 A combination of "black box" and "calendar-time" methods for the determination of calibration intervals of an analytical measuring instrument is discussed. Since the methods require information on the distributions of the calibration parameters, such information is described for an atomic absorption spectrophotometer, as an example. The hypotheses on the normal distribution of the calibration parameters are tested using the ω²-criterion and accepted at 0.90–0.95 levels of confidence. Corresponding control charts are designed for indication of warning and action limits of the calibration parameters, and diagnoses of outliers in further calibrations. Control charts indicate also when the calibration should be done according to the full program of the equipment manufacturer. Received: 15 April 2000 / Accepted: 24 July 2000     

Consensus,Polarization and Hysteresis in the Three-State Noisy q-Voter Model with Bounded Confidence

In this work, we address the question of the role of the influence of group size on the emergence of various collective social phenomena, such as consensus, polarization and social hysteresis. To answer this question, we study the three-state noisy q-voter model with bounded confidence, in which agents can be in one of three states: two extremes (leftist and rightist) and centrist. We study the model on a complete graph within the mean-field approach and show that, depending on the size q of the influence group, saddle-node bifurcation cascades of different length appear and different collective phenomena are possible. In particular, for all values of q>1, social hysteresis is observed. Furthermore, for small values of q∈(1,4), disagreement, polarization and domination of centrists (a consensus understood as the general agreement, not unanimity) can be achieved but not the domination of extremists. The latter is possible only for larger groups of influence. Finally, by comparing our model to others, we discuss how a small change in the rules at the microscopic level can dramatically change the macroscopic behavior of the model.     

巴斯卡分布参数p的置信区间

讨论了巴斯卡分布与Beta分布的联系,并通过F分布的分位点给出了参数p的置信水平为1-α的置信区间.     

Distribution function estimates by Wasserstein metric and Bernstein approximation for C-1 functions

The aim of the paper is to estimate the density functions or distribution functions measured by Wasserstein metric, a typical kind of statistical distances, which is usually required in the statistical learningBased on the classical Bernstein approximation, a scheme is presented.To get the error estimates of the scheme, the problem turns to estimating the L1 norm of the Bernstein approximation for monotone C-1functions, which was rarely discussed in the classical approximation theoryFinally, we get a probability estimate by the statistical distance.     

基于属性识别准则大学生思想品德量化的数学模型

依据一定的社会评价标准,建立大学生思想品德评价的指标体系,利用现代数学方法——属性识别理论和层次分析方法,建立定量研究模型.     

农残水平测试中数据多态性分析及指定值估计研究

对全国农残水平测试中毒死蜱、氯氰菊酯数据进行统计分析,在数据统计分布特征研究基础上,使用内核密度估计进行数据多态性分析,使用bootstrap模拟取样法对数据样本值重复取样,以获得稳健的水平测试样品待测物含量代表值估计、标准误差及置信区间描述,证明以bootstrap模拟取样法获取的均值与标准偏差作为有限单次样本代表值是合理、有效的,解决了四分位稳健统计方法对非正态多态分布代表值估计不稳定问题及取样理论中取样样本数限制的瓶颈,为能力验证计划指定值的获取提供了一种新方法。     

The Effects of Formulation on Imidacloprid Dissipation in Grapes and Vine Leaves and on Required Pre-Harvest Intervals under Lebanese Climatic Conditions

In this study, imidacloprid, a systemic insecticide, currently having a specified European Commission MRL value for vine leaves (2 mg kg⁻¹), was applied on a Lebanese vineyard under different commercial formulations: as a soluble liquid (SL) and water dispersible granules (WDG). In Lebanon, many commercial formulations of imidacloprid are subject to the same critical good agricultural practice (cGAP). It was, therefore, important to verify the variability in dissipation patterns according to matrix nature and formulation type. Random samplings of grapes and vine leaves were performed starting at 2 days until 18 days after treatment. Residue extractions were performed according to the QuEChERS method and the analytical determination using liquid chromatography coupled to tandem mass spectrometry (LC-MS-MS). The SL formulation yielded significantly higher initial deposit than the WDG formulation on grapes and vine leaves. The formulation type did not significantly affect the dissipation rates; the estimated half-lives in grapes and vine leaves were 0.5 days for all imidacloprid formulations. No pre-harvest intervals were necessary on grapes. PHIs of 3.7 days for the SL formulation and 2.8 days for the WDG formulation were estimated on vine leaves. The results showed that the type of formulation and the morphological and physiological characteristics of the matrix had an effect on the initial deposits, and thus residue levels, but not on the dissipation patterns.     

矿产品水分含量代表值Bootstrap模拟取样估计

在对矿产品水分含量基础统计学特征描述的基础上,采用内核密度估计对水分含量数据多态性进行了分析,根据双态分布的特点,使用Bootstrap模拟取样方法对试验样本值模拟重复取样,以多次Bootstrap模拟取样的均值与标准偏差作为矿产品水分含量有限样本代表值及标准偏差的稳健估计,实践证明Bootstrap模拟取样估计对矿产品水分含量代表值的估计是有效的,该项研究为矿产品水分含量代表值的准确评估提供了一种新方法.