Time series models with asymmetric innovations

We consider AR(q) models in time series with asymmetric innovations represented by two families ofdistributions: (i) gamma with support IR : (0, ∞), and (ii) generalized logistic with support IR:(-∞,∞). Since the ML (maximum likelihood) estimators are intractable, we derive the MML (modified maximum likelihood) estimators of the parameters and show that they are remarkably efficient besides being easy to compute. We investigate the efficiency properties of the classical LS (least squares) estimators. Their efficiencies relative to the proposed MML estimators are very low.     

Normality testing for a long-memory sequence using the empirical moment generating function

Moment generating functions and more generally, integral transforms for goodness-of-fit tests have been in use in the last several decades. Given a set of observations, the empirical transforms are easy to compute, being simply a sample mean, and due to uniqueness properties, these functions can be used for goodness-of-fit tests. This paper focuses on time series observations from a stationary process for which the moment generating function exists and the correlations have long-memory. For long-memory processes, the infinite sum of the correlations diverges and the realizations tend to have spurious trend like patterns where there may be none. Our aim is to use the empirical moment generating function to test the null hypothesis that the marginal distribution is Gaussian. We provide a simple proof of a central limit theorem using ideas from Gaussian subordination models (Taqqu, 1975) and derive critical regions for a graphical test of normality, namely the T₃-plot ( Ghosh, 1996). Some simulated and real data examples are used for illustration.     

Three-Factor Cartographic Representation

Statistics and statisticians have contributed to industry. Attention has been given to the appropriate training of statisticians for careers in industry. Statistics is used with benefit to industry in quality control, experimental design in research and development, and management decisions. Statistics can benefit from industry's assistance, the subject of this article. Five premises are set forth, three of them suggesting problems for statistics and industry. They relate to public understanding of statistics, the recruitment of students to statistics, the recruitment of statisticians to industry, and the relevance of research in statistics to the needs of industry. Thirteen recommendations are made on what industry can do for statistics and suggestions are made on how the American Statistical Association and the American Society for Quality Control can provide leadership in meeting the problems posed with the help of industry.     

不确定交货条件下供应链协调的 Stackelberg 对策研究

研究了在不确定交货条件下的一种供应链协调机制———Stackelberg 主从对策. 供应链中 的生产商作为主方,以成本最小为目标给出最佳的订货量和惩罚成本策略;供应商作为从方, 以使其效益最大化的最佳额外生产能力作为响应策略. 最后,以上海宝钢集团企业开发总公司 的尾板卷深加工为实际背景,采用遗传算法进行了仿真计算,结果表明主从对策的供应链协调 机制的有效性.     

Bayesian inference for the generalized exponential distribution

The two-parameter generalized exponential (GE) distribution was introduced by Gupta and Kundu [Gupta, R.D. and Kundu, D., 1999, Generalized exponential distribution. Australian and New Zealand Journal of Statistics, 41(2), 173–188.]. It was observed that the GE can be used in situations where a skewed distribution for a nonnegative random variable is needed. In this article, the Bayesian estimation and prediction for the GE distribution, using informative priors, have been considered. Importance sampling is used to estimate the parameters, as well as the reliability function, and the Gibbs and Metropolis samplers data sets are used to predict the behavior of further observations from the distribution. Two data sets are used to illustrate the Bayesian procedure.     

Testing for concordance between several criteria

The problem of whether the rankings of some objects given by a set of criteria (or judges) show any agreement or are more or less independent is addressed. The most familiar measure for concordance is the Kendall W coefficient. Classical tests for concordance are the Friedman test and the F test. Legendre [Species associations: the Kendall coefficient of concordance revisited. J. Agric. Biol. Environ. Stat. 2005;10(2):226–245] compared via simulation the Friedman test and its permutation version. Unfortunately, the simulation study of Legendre was very limited because it considered neither the copula aspect nor the F test. Kendall W is a rank-based correlation measure, and therefore it is not affected by the marginal distributions of the underlying variables, but only by the copula of the multivariate distribution. In this article, the simulation study of Legendre is deeply extended by considering the copula aspect as well as the F test. It is shown that the Friedman test is too conservative and less powerful than both the F test and the permutation test for concordance which always have a correct size and behave alike. The F test should be preferred because it is computationally much easier. Surprisingly, the power function of the tests is not much affected by the type of copula.     

Simultaneous rank tests for detecting differentially expressed genes

Rank tests are known to be robust to outliers and violation of distributional assumptions. Two major issues besetting microarray data are violation of the normality assumption and contamination by outliers. In this article, we formulate the normal theory simultaneous tests and their aligned rank transformation (ART) analog for detecting differentially expressed genes. These tests are based on the least-squares estimates of the effects when data follow a linear model. Application of the two methods are then demonstrated on a real data set. To evaluate the performance of the aligned rank transform method with the corresponding normal theory method, data were simulated according to the characteristics of a real gene expression data. These simulated data are then used to compare the two methods with respect to their sensitivity to the distributional assumption and to outliers for controlling the family-wise Type I error rate, power, and false discovery rate. It is demonstrated that the ART generally possesses the robustness of validity property even for microarray data with small number of replications. Although these methods can be applied to more general designs, in this article the simulation study is carried out for a dye-swap design since this design is broadly used in cDNA microarray experiments.     

Stress testing correlation matrix: a maximum empirical likelihood approach

ABSTRACT

Stress testing correlation matrix is a challenging exercise for portfolio risk management. Most existing methods directly modify the estimated correlation matrix to satisfy stress conditions while maintaining positive semidefiniteness. The focus lies on technical optimization issues but the resultant stressed correlation matrices usually lack statistical interpretations. In this article, we suggest a novel approach using Empirical Likelihood method to modify the probability weights of sample observations to construct a stressed correlation matrix. The resultant correlations correspond to a stress scenario that is nearest to the observed scenario in a Kullback–Leibler divergence sense. Besides providing a clearer statistical interpretation, the proposed method is non-parametric in distribution, simple in computation and free from subjective tunings. We illustrate the method through an application to a portfolio of international assets.