Comparing a new Gini test with other symmetry tests when median is known

ABSTRACT

Wang et al. (2013 Wang, J. C., H. Auda, and M. Niewiadomska-Bugaj. 2013. Comparing a new Gini test with other symmetry tests when median is unknown. Communications in Statistics- Simulation and Computation 42:1616–27.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) provided a comprehensive study of 14 tests, including two tests based on the Gini mean difference (GMD) introduced by Auda (2006), applicable for data from populations with an unknown median. This paper is a similar study of symmetry tests applicable for data from populations with a known median. We are showing that GMD tests compare favorably with several existing procedures in controlling the type I error as well as in power. Results of the study are shown graphically, which makes the tests’ power easy to assess.     

On a control chart for the Gini index with simulations

In this work we suggest the use of the Gini index on control charts. The asymptotic properties of Gini index are presented and the control charts based on appropriate confidence intervals are constructed. The suitability of the proposed charts are investigated by means of extensive simulations.     

On Unit-Root Tests When the Alternative Is a Trend-Break Stationary Process

Minimum t statistics to test for a unit-root are available when the form of break under the alternative evolves according to the crash, changing growth, and mixed models. It is shown that serious power distortions occur if the form of break is misspecified, and thus the practitioner should use the mixed model as the appropriate alternative in empirical applications. The mixed model may reveal useful information regarding the location and form of break. The maximum F statistic for the joint null of a unit-root and no breaks is shown to have greater and less erratic power compared to the minimumt statistic. Stronger evidence against the unit-root is found for the Nelson-Plosser series and U.S. Postwar quarterly real gross national product.     

Tests for Serial Dependence and Other Specification Analysis in Models of Markets in Disequilibrium

The assumption of serial independence of disturbances is the starting point of most of the work done on analyzing market disequilibrium models. We derive tests for serial dependence given normality and homoscedasticity using the Lagrange multiplier (LM) test principle. Although the likelihood function under serial dependence is very complicated and involves multiple integrals of dimensions equal to the sample size, the test statistic we obtain through the LM principle is very simple. We apply the test to the housing-start data of Fair and Jaffee (1972) and study its finite sample properties through simulation. The test seems to perform quite well in finite samples in terms of size and power. We present an analysis of disequilibrium models that assumes that the disturbances are logistic rather than normal. The relative performances of these distributions are investigated by simulation.     

Normality Test Based on a Truncated Mean Characterization

This article generalizes a characterization based on a truncated mean to include higher truncated moments, and introduces a new normality goodness-of-fit test based on the truncated mean. The test is a weighted integral of the squared distance between the empirical truncated mean and its expectation. A closed form for the test statistic is derived. Assuming known parameters, the mean and the variance of the test are derived under the normality assumption. Moreover, a limiting distribution for the proposed test as well as an approximation are obtained. Also, based on Monte Carlo simulations, the power of the test is evaluated against stable, symmetric, and skewed classes of distributions. The test proves compatibility with prominent tests and shows higher power for a wide range of alternatives.     

Some New Residual Treatment Effects Designs for Comparing Test Treatments with a Control

Pigeon & Raghavarao (1987) introduced control balanced residual treatment effects designs for the situation where one treatment is a control or standard and is to be compared with the v test treatments, and they have also given methods of construction of control balanced residual treatment effects designs and have investigated their efficiencies. In this paper we have developed some new families of control balanced residual treatment effects designs, which are Schur-optimal.