A statistical uncertainty principle for estimating the time of a discrete shift in the mean of a continuous time random process

The purpose of this article is to present a statistical uncertainty principle that can be used when localizing a single change in the mean of a band-limited stationary random process. The statistical model investigated is a continuous time process that experiences a shift in its mean. This continuous time process is presumed to be sampled using an ideal low-pass filter. The least squares estimate of the location of the change in mean is asymptotically Gaussian. The standard deviation of the least squares estimate of the location of the change-point provides a physical limit to the accuracy of the estimate of the time of the mean shift which cannot be bettered.     

Optimal Experimental Design Strategies for Detecting Hormesis

Hormesis is a widely observed phenomenon in many branches of life sciences, ranging from toxicology studies to agronomy, with obvious public health and risk assessment implications. We address optimal experimental design strategies for determining the presence of hormesis in a controlled environment using the recently proposed Hunt‐Bowman model. We propose alternative models that have an implicit hormetic threshold, discuss their advantages over current models, and construct and study properties of optimal designs for (i) estimating model parameters, (ii) estimating the threshold dose, and (iii) testing for the presence of hormesis. We also determine maximin optimal designs that maximize the minimum of the design efficiencies when we have multiple design criteria or there is model uncertainty where we have a few plausible models of interest. We apply these optimal design strategies to a teratology study and show that the proposed designs outperform the implemented design by a wide margin for many situations.     

评分方法在大学英语写作形成性评估中效应实证研究——整体评分与混合评分方法对比分析

基于形成性评价工具Writing Roadmap,针对评定学生写作文本时所采用的评分方式,分析在形成性评估过程中混合法和单纯的整体法评分方法对学习者写作水平提高的影响程度。实验对象为63名大学英语学习者。研究方法为观察法和量化统计法,并使用SPSS统计软件对写作成绩进行对比分析。研究表明,在大学英语写作形成性评估过程中,使用分项式和整体评分相结合的混合评分法更有助于促进学习者的写作水平的提高,并据此提出在写作形成性评估中设定混合评分标准应考虑的因素。     

Selecting the Optimal Transformation of a Continuous Covariate in Cox's Regression: Implications for Hypothesis Testing

ABSTRACT

Background: Many exposures in epidemiological studies have nonlinear effects and the problem is to choose an appropriate functional relationship between such exposures and the outcome. One common approach is to investigate several parametric transformations of the covariate of interest, and to select a posteriori the function that fits the data the best. However, such approach may result in an inflated Type I error. Methods: Through a simulation study, we generated data from Cox's models with different transformations of a single continuous covariate. We investigated the Type I error rate and the power of the likelihood ratio test (LRT) corresponding to three different procedures that considered the same set of parametric dose-response functions. The first unconditional approach did not involve any model selection, while the second conditional approach was based on a posteriori selection of the parametric function. The proposed third approach was similar to the second except that it used a corrected critical value for the LRT to ensure a correct Type I error. Results: The Type I error rate of the second approach was two times higher than the nominal size. For simple monotone dose-response, the corrected test had similar power as the unconditional approach, while for non monotone, dose-response, it had a higher power. A real-life application that focused on the effect of body mass index on the risk of coronary heart disease death, illustrated the advantage of the proposed approach. Conclusion: Our results confirm that a posteriori selecting the functional form of the dose-response induces a Type I error inflation. The corrected procedure, which can be applied in a wide range of situations, may provide a good trade-off between Type I error and power.     

An Empirical Nonlinear Data-Fitting Approach for Transforming Data to Normality

A general method is proposed by which nonnormally distributed data can be transformed to achieve approximate normality. The method uses an empirical nonlinear data-fitting approach and can be applied to a broad class of transformations including the Box-Cox, arcsine, generalized logit, and Weibull-type transformations. It is easy to implement using standard statistical software packages. Several examples are provided.     

A semiparametric Bayesian approach to simplex regression model with heterogeneous dispersion

ABSTRACT

Simplex regression model is often employed to analyze continuous proportion data in many studies. In this paper, we extend the assumption of a constant dispersion parameter (homogeneity) to varying dispersion parameter (heterogeneity) in Simplex regression model, and present the B-spline to approximate the smoothing unknown function within the Bayesian framework. A hybrid algorithm combining the block Gibbs sampler and the Metropolis-Hastings algorithm is presented for sampling observations from the posterior distribution. The procedures for computing model comparison criteria such as conditional predictive ordinate statistic, deviance information criterion, and averaged mean squared error are presented. Also, we develop a computationally feasible Bayesian case-deletion influence measure based on the Kullback-Leibler divergence. Several simulation studies and a real example are employed to illustrate the proposed methodologies.     

The Homogeneous Markov System (HMS) as an Elastic Medium. The Three-Dimensional Case

Every attainable structure of the so-called continuous-time Homogeneous Markov System (HMS) with fixed size and state space S = {1, 2,…, n} is considered as a particle of R ⁿ and, consequently, the motion of the structure corresponds to the motion of the particle. Under the assumption that “the motion of every particle-structure at every time point is due to its interaction with its surroundings,” R ⁿ becomes a continuum (Tsaklidis, 1998 Tsaklidis , G. ( 1998 ). The continuous time homogeneous Markov system with fixed size as a Newtonian fluid? Appl. Stoch. Mod. Data Anal. 13 : 177 – 182 .[Crossref] , [Google Scholar]). Then the evolution of the set of the attainable structures corresponds to the motion of the continuum. For the case of a three-state HMS it is stated that the concept of the two-dimensional isotropic elasticity can further be used to interpret the three-state HMS's evolution.     

A statistical model of tracking

A method is proposed to model individual patterns of growth over time by linear combinations of optimally chosen weighted orthogonal vectors. The goal is to distinguish individuals who track from nontrackers. Nontrackers are defined as those who follow different, usually more complex, growth patterns than trackers. Thus, nontrackers require more vectors than do trackers in modeling their longitudinal observations. A method of specifying the class-specific vectors and individual weights is demonstrated. When the proportion of nontrackers in the population is small, a modified form of the Akaike maximum entropy criterion is used to select the number of vectors appopriate for each person and also to classify each person into a tracking category. When the proportion of nontrackers is large, the modified Akaike criterion together with scatterplots of the growth curve weights are needed to distinguish trackers from nontrackers. The apprach is illustrated with longitudinal observations of height measured in an epidemiologic survey of children.     

Linear signed rank tests for hultivariate location

Previously proposed linear signed rank tests for multivariate location are not invariant under linear transformations of the observations, The asymptotic relative efficiencies of the tests 2 with respect to Hotelling's T²test depend on the direction of shift and the covariance matrix of the alternative distributions. For distributions with highly correlated components, the efficiencies of some of these tests can be arbitrarily low; they approach zero for certain multivariate normal alternatives, This article proposes a transformation of the data to be performed prior to standard linear signed rank tests, The resulting procedures have attractive power and efficiency properties compared to the original tests, In particular, for elliptically symmetric contiguous alternafives, the efficiencies of the new tests equal those of corresponding univariate linear signed rank tests with respect to the t test.