A multivariate zero-inflated binomial model for the analysis of correlated proportional data

In this paper, a new multivariate zero-inflated binomial (MZIB) distribution is proposed to analyse the correlated proportional data with excessive zeros. The distributional properties of purposed model are studied. The Fisher scoring algorithm and EM algorithm are given for the computation of estimates of parameters in the proposed MZIB model with/without covariates. The score tests and the likelihood ratio tests are derived for assessing both the zero-inflation and the equality of multiple binomial probabilities in correlated proportional data. A limited simulation study is performed to evaluate the performance of derived EM algorithms for the estimation of parameters in the model with/without covariates and to compare the nominal levels and powers of both score tests and likelihood ratio tests. The whitefly data is used to illustrate the proposed methodologies.     

具有GARCH（1，1）-正态误差项的非对称单位根检验研究

摘　　要:理论研究表明许多经济变量呈现出非对称的门限自回归（TAR）或动态门限自回归（M-TAR）数据生成机制,因而非对称单位根检验就成为该领域的主要研究方向之一。本文对非对称单位根检验Enders-Granger方法在GARCH（1,1）-正态误差项下的检验水平与检验势作了系统的仿真研究。研究表明：GARCH（1,1）-正态误差项的TAR或M-TAR模型会对该方法的检验水平和检验势产生重要影响。     

A win ratio approach to comparing continuous non‐normal outcomes in clinical trials

Clinical trials are often designed to compare continuous non‐normal outcomes. The conventional statistical method for such a comparison is a non‐parametric Mann–Whitney test, which provides a P‐value for testing the hypothesis that the distributions of both treatment groups are identical, but does not provide a simple and straightforward estimate of treatment effect. For that, Hodges and Lehmann proposed estimating the shift parameter between two populations and its confidence interval (CI). However, such a shift parameter does not have a straightforward interpretation, and its CI contains zero in some cases when Mann–Whitney test produces a significant result. To overcome the aforementioned problems, we introduce the use of the win ratio for analysing such data. Patients in the new and control treatment are formed into all possible pairs. For each pair, the new treatment patient is labelled a ‘winner’ or a ‘loser’ if it is known who had the more favourable outcome. The win ratio is the total number of winners divided by the total numbers of losers. A 95% CI for the win ratio can be obtained using the bootstrap method. Statistical properties of the win ratio statistic are investigated using two real trial data sets and six simulation studies. Results show that the win ratio method has about the same power as the Mann–Whitney method. We recommend the use of the win ratio method for estimating the treatment effect (and CI) and the Mann–Whitney method for calculating the P‐value for comparing continuous non‐Normal outcomes when the amount of tied pairs is small. Copyright © 2016 John Wiley & Sons, Ltd.     

Testing Overdispersion in CUBE Models

A practical problem with large-scale survey data is the possible presence of overdispersion. It occurs when the data display more variability than is predicted by the variance–mean relationship. This article describes a probability distribution generated by a mixture of discrete random variables to capture uncertainty, feeling, and overdispersion. Specifically, several tests for detecting overdispersion will be implemented on the basis of the asymptotic theory for maximum likelihood estimators. We discuss the results of a simulation experiment concerning log-likelihood ratio, Wald, Score, and Profile tests. Finally, some real datasets are analyzed to illustrate the previous results.     

Intraday Serial Correlation,Volatility, and Jump: Evidence from China's Stock Market

In this article, we investigate the relationships among intraday serial correlation, jump-robust volatility, positive and negative jumps based on Shanghai composite index high frequency data. We implement variance ratio test to quantify intraday serial correlation. We also measure the continuous part of realized volatility using jump-robust MedRV estimator and disentangle positive and negative jumps using Realized Downside Risk Measure and Realized Upside Potential Measure proposed by Bi et al., (2013 Bi, T., Zhang, B., Wu, H. (2013). Measuring downside risk using high frequency data–realized downside risk measure. Communications in Statistics–Simulation and Computation 42(4):741–754.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]). We find that intraday serial correlation are positively correlated with jump-robust volatility and negatively correlated with negative jumps which confirm the LeBaron effect.     

An Automatic Test for the Umbrella Alternatives

The paper proposes a new test for detecting the umbrella pattern under a general non‐parametric scheme. The alternative asserts that the umbrella ordering holds while the hypothesis is its complement. The main focus is put on controlling the power function of the test outside the alternative. As a result, the asymptotic error of the first kind of the constructed solution is smaller than or equal to the fixed significance level α on the whole set where the umbrella ordering does not hold. Also, under finite sample sizes, this error is controlled to a satisfactory extent. A simulation study shows, among other things, that the new test improves upon the solution widely recommended in the literature of the subject. A routine, written in R, is attached as the Supporting Information file.     

Pooled Panel Unit Root Tests and the Effect of Past Initialization

This paper analyzes the role of initialization when testing for a unit root in panel data, an issue that has received surprisingly little attention in the literature. In fact, most studies assume that the initial value is either zero or bounded. As a response to this, the current paper considers a model in which the initialization is in the past, which is shown to have several distinctive features that makes it attractive, even in comparison to the common time series practice of making the initial value a draw from its unconditional distribution under the stationary alternative. The results have implications not only for theory, but also for applied work. In particular, and in contrast to the time series case, in panels the effect of the initialization need not be negative but can actually lead to improved test performance.     

Imposing and Testing for Shape Restrictions in Flexible Parametric Models

In many economic models, theory restricts the shape of functions, such as monotonicity or curvature conditions. This article reviews and presents a framework for constrained estimation and inference to test for shape conditions in parametric models. We show that “regional” shape-restricting estimators have important advantages in terms of model fit and flexibility (as opposed to standard “local” or “global” shape-restricting estimators). In our empirical illustration, this is the first article to impose and test for all shape restrictions required by economic theory simultaneously in the “Berndt and Wood” data. We find that this dataset is consistent with “duality theory,” whereas previous studies have found violations of economic theory. We discuss policy consequences for key parameters, such as whether energy and capital are complements or substitutes.     

The Local Power of the CADF and CIPS Panel Unit Root Tests

Very little is known about the local power of second generation panel unit root tests that are robust to cross-section dependence. This article derives the local asymptotic power functions of the cross-section argumented Dickey–Fuller Cross-section Augmented Dickey-Fuller (CADF) and CIPS tests of Pesaran (2007), which are among the most popular tests around.     

A nonparametric hypothesis test for heteroscedasticity

In this paper, a hypothesis test for heteroscedasticity is proposed in a nonparametric regression model. The test statistic, which uses the residuals from a nonparametric fit of the mean function, is based on an adaptation of the well-known Levene's test. Using the recent theory for analysis of variance when the number of factor levels goes to infinity, the asymptotic distribution of the test statistic is established under the null hypothesis of homocedasticity and under local alternatives. Simulations suggest that the proposed test performs well in several situations, especially when the variance is a nonlinear function of the predictor.