Inferences on the Means of Two Log-Normal Distributions: A Computational Approach Test

In this article, we propose a novel approach for testing the equality of two log-normal populations using a computational approach test (CAT) that does not require explicit knowledge of the sampling distribution of the test statistic. Simulation studies demonstrate that the proposed approach can perform hypothesis testing with satisfying actual size even at small sample sizes. Overall, it is superior to other existing methods. Also, a CAT is proposed for testing about reliability of two log-normal populations when the means are the same. Simulations show that the actual size of this new approach is close to nominal level and better than the score test. At the end, the proposed methods are illustrated using two examples.     

Testing equality of two normal covariance matrices with monotone missing data

Abstract

The problem of testing equality of two multivariate normal covariance matrices is considered. Assuming that the incomplete data are of monotone pattern, a quantity similar to the Likelihood Ratio Test Statistic is proposed. A satisfactory approximation to the distribution of the quantity is derived. Hypothesis testing based on the approximate distribution is outlined. The merits of the test are investigated using Monte Carlo simulation. Monte Carlo studies indicate that the test is very satisfactory even for moderately small samples. The proposed methods are illustrated using an example.     

疲劳裂纹扩展试验裂纹图像采集系统

针对目前金属疲劳裂纹扩展检测方法存在效率低、操作繁琐、精度不高，不能实现实时性等缺点，文章提出了基 于机器视觉的裂纹检测方法。根据金属疲劳裂纹扩展试验过程中裂纹图像的采集要求，设计了摄像头位置可自动调整 的疲劳裂纹图像采集系统，包括摄像头安装运动装置，裂纹图像采集装置以及摄像头运动控制系统。图像采集装置由高 分辨率黑白面阵CCD摄像头、光学镜头，光源照明装置和图像采集卡组成，前3者安装在摄像头支架上，与摄像头运动 装置相连。摄像头运动装置中的X，Y，，Z轴运动机构由步进电机带动滚珠导轨机构。在基于ARM技术的运动控制系统 的控制下摄像头可沿X，Y，，Z轴作高精度直线运动，实现和试件之间精确位置的调整。实验结果表明，所设计的系统可 采集到疲劳裂纹扩展试验过程中高清晰度、高分辨率的试件裂纹图像，满足下一步裂绞尺寸计算的要求；摄像头运动定 位精度可达到0. 02 mm，满足精确的系统聚焦、位置调整、跟踪采集的要求。     

Inference and optimal design of multiple constant-stress testing for generalized half-normal distribution under type-II progressive censoring

The generalized half-normal (GHN) distribution and progressive type-II censoring are considered in this article for studying some statistical inferences of constant-stress accelerated life testing. The EM algorithm is considered to calculate the maximum likelihood estimates. Fisher information matrix is formed depending on the missing information law and it is utilized for structuring the asymptomatic confidence intervals. Further, interval estimation is discussed through bootstrap intervals. The Tierney and Kadane method, importance sampling procedure and Metropolis-Hastings algorithm are utilized to compute Bayesian estimates. Furthermore, predictive estimates for censored data and the related prediction intervals are obtained. We consider three optimality criteria to find out the optimal stress level. A real data set is used to illustrate the importance of GHN distribution as an alternative lifetime model for well-known distributions. Finally, a simulation study is provided with discussion.     

Random effects regression mixtures for analyzing infant habituation

Random effects regression mixture models are a way to classify longitudinal data (or trajectories) having possibly varying lengths. The mixture structure of the traditional random effects regression mixture model arises through the distribution of the random regression coefficients, which is assumed to be a mixture of multivariate normals. An extension of this standard model is presented that accounts for various levels of heterogeneity among the trajectories, depending on their assumed error structure. A standard likelihood ratio test is presented for testing this error structure assumption. Full details of an expectation-conditional maximization algorithm for maximum likelihood estimation are also presented. This model is used to analyze data from an infant habituation experiment, where it is desirable to assess whether infants comprise different populations in terms of their habituation time.     

Tests for time series of counts based on the probability-generating function

We propose testing procedures for the hypothesis that a given set of discrete observations may be formulated as a particular time series of counts with a specific conditional law. The new test statistics incorporate the empirical probability-generating function computed from the observations. Special emphasis is given to the popular models of integer autoregression and Poisson autoregression. The asymptotic properties of the proposed test statistics are studied under the null hypothesis as well as under alternatives. A Monte Carlo power study on bootstrap versions of the new methods is included as well as real-data examples.     

Computing maximum likelihood estimates from type II doubly censored exponential data

It is well-known that, under Type II double censoring, the maximum likelihood (ML) estimators of the location and scale parameters, θ and δ, of a twoparameter exponential distribution are linear functions of the order statistics. In contrast, when θ is known, theML estimator of δ does not admit a closed form expression. It is shown, however, that theML estimator of the scale parameter exists and is unique. Moreover, it has good large-sample properties. In addition, sharp lower and upper bounds for this estimator are provided, which can serve as starting points for iterative interpolation methods such as regula falsi. Explicit expressions for the expected Fisher information and Cramér-Rao lower bound are also derived. In the Bayesian context, assuming an inverted gamma prior on δ, the uniqueness, boundedness and asymptotics of the highest posterior density estimator of δ can be deduced in a similar way. Finally, an illustrative example is included.     

GMM tests for the Katz family of distributions

Generalized method of moments (GMM) is used to develop tests for discriminating discrete distributions among the two-parameter family of Katz distributions. Relationships involving moments are exploited to obtain identifying and over-identifying restrictions. The asymptotic relative efficiencies of tests based on GMM are analyzed using the local power approach and the approximate Bahadur efficiency. The paper also gives results of Monte Carlo experiments designed to check the validity of the theoretical findings and to shed light on the small sample properties of the proposed tests. Extensions of the results to compound Poisson alternative hypotheses are discussed.     

Merging information for semiparametric density estimation

Summary.  The density ratio model specifies that the likelihood ratio of m −1 probability density functions with respect to the m th is of known parametric form without reference to any parametric model. We study the semiparametric inference problem that is related to the density ratio model by appealing to the methodology of empirical likelihood. The combined data from all the samples leads to more efficient kernel density estimators for the unknown distributions. We adopt variants of well-established techniques to choose the smoothing parameter for the density estimators proposed.     

ASSESSING CONGRUENCEAMONG DISTANCE MATRICES: SINGLE-MALT SCOTCH WHISKIES REVISITED

A test of congruence among distance matrices is described. It tests the hypothesis that several matrices, containing different types of variables about the same objects, are congruent with one another, so they can be used jointly in statistical analysis. Raw data tables are turned into similarity or distance matrices prior to testing; they can then be compared to data that naturally come in the form of distance matrices. The proposed test can be seen as a generalization of the Mantel test of matrix correspondence to any number of distance matrices. This paper shows that the new test has the correct rate of Type I error and good power. Power increases as the number of objects and the number of congruent data matrices increase; power is higher when the total number of matrices in the study is smaller. To illustrate the method, the proposed test is used to test the hypothesis that matrices representing different types of organoleptic variables (colour, nose, body, palate and finish) in single‐malt Scotch whiskies are congruent.