边限检验理论及几点讨论

检验经济变量之间长期关系的协整技术要求变量是同阶单整的,这不可避免地涉及一定程度的预检验问题,而预检验问题会增加变量间长期关系分析的不确定性。当不能确定变量的单整类型时,边限检验理论提出了一个可以直接检验一个变量和一组解释变量之间长期关系的新方法。在介绍了边限检验方法中基本的VAR模型和假设及边限检验方法中用到的重要统计量——Wald统计量和T统计量及它们各自的渐近分布形式后,说明了边限检验理论在理论和实际运用当中需要注意的几个问题,最后通过实例分析说明了边限检验理论的运用。     

Using the integrative model of behavioral prediction to understand college students’ STI testing beliefs,intentions, and behaviors

ABSTRACT

Objectives: To identify salient behavioral determinants related to STI testing among college students by testing a model based on the integrative model of behavioral (IMBP) prediction. Participants: 265 undergraduate students from a large university in the Southeastern US. Methods:Formative and survey research to test an IMBP-based model that explores the relationships between determinants and STI testing intention and behavior. Results: of path analyses supported a model in which attitudinal beliefs predicted intention and intention predicted behavior. Normative beliefs and behavioral control beliefs were not significant in the model; however, select individual normative and control beliefs were significantly correlated with intention and behavior. Conclusions: Attitudinal beliefs are the strongest predictor of STI testing intention and behavior. Future efforts to increase STI testing rates should identify and target salient attitudinal beliefs.     

Testing hypotheses about the common mean of two normal populations

Two simple tests which allow for unequal sample sizes are considered for testing hypothesis for the common mean of two normal populations. The first test is an exact test of size a based on two available t-statistics based on single samples made exact through random allocation of α among the two available t-tests. The test statistic of the second test is a weighted average of two available t-statistics with random weights. It is shown that the first test is more efficient than the available two t-tests with respect to Bahadur asymptotic relative efficiency. It is also shown that the null distribution of the test statistic in the second test, which is similar to the one based on the normalized Graybill-Deal test statistic, converges to a standard normal distribution. Finally, we compare the small sample properties of these tests, those given in Zhou and Mat hew (1993), and some tests given in Cohen and Sackrowitz (1984) in a simulation study. In this study, we find that the second test performs better than the tests given in Zhou and Mathew (1993) and is comparable to the ones given in Cohen and Sackrowitz (1984) with respect to power..     

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.     

The Economic Efficiency of Sampling Size: The Case of Beef Trim

The economically optimal sample size in a food safety test balances the marginal costs and marginal benefits of increasing the sample size. We provide a method for selecting the sample size when testing beef trim for Escherichia coli O157:H7 that equates the averted costs of recalls and health damages from contaminated meats sold to consumers with the increased costs of testing while allowing for uncertainty about the underlying prevalence rates of contamination. Using simulations, we show that, in most cases, the optimal sample size is larger than the current sample size of 60 and, in some cases, it exceeds 120. Moreover, lots with a lower prevalence rate have a higher expected damage because contamination is more difficult to detect. Our simulations indicate that these lots have a higher optimal sampling rate.     

Bootstrap Testing of Hypotheses on Co‐Integration Relations in Vector Autoregressive Models

It is well known that the finite‐sample properties of tests of hypotheses on the co‐integrating vectors in vector autoregressive models can be quite poor, and that current solutions based on Bartlett‐type corrections or bootstrap based on unrestricted parameter estimators are unsatisfactory, in particular in those cases where also asymptotic χ² tests fail most severely. In this paper, we solve this inference problem by showing the novel result that a bootstrap test where the null hypothesis is imposed on the bootstrap sample is asymptotically valid. That is, not only does it have asymptotically correct size, but, in contrast to what is claimed in existing literature, it is consistent under the alternative. Compared to the theory for bootstrap tests on the co‐integration rank (Cavaliere, Rahbek, and Taylor, 2012), establishing the validity of the bootstrap in the framework of hypotheses on the co‐integrating vectors requires new theoretical developments, including the introduction of multivariate Ornstein–Uhlenbeck processes with random (reduced rank) drift parameters. Finally, as documented by Monte Carlo simulations, the bootstrap test outperforms existing methods.     

A survey on nonadaptive group testing algorithms through the angle of decoding

Group testing, sometimes called pooling design, has been applied to a variety of problems such as blood testing, multiple access communication, coding theory, among others. Recently, screening experiments in molecular biology has become the most important application. In this paper, we review several models in this application by focusing on decoding, namely, giving a comparative study of how the problem is solved in each of these models.     

Hypothesis group testing for disjoint pairs

Classical group testing (CGT) is a widely applicable biotechnical technique used to identify a small number of distinguished objects from a population when the presence of any one of these distinguished objects among a group of others produces an observable result. This paper discusses a variant of CGT called group testing for disjoint pairs (GTAP). The difference between the two is that in GTDP, the distinguished items are pairs from, not individual objects in, the population. There are several biological examples of when this abstract model applies. One biological example is DNA hybridization. The presence of pairs of hybridized DNA strands can be detected in a pool of DNA strands. Another situation is the detection of binding interactions between prey and bait proteins. This paper gives a random pooling method, similar in spirit to hypothesis testing, which identifies pairs of objects from a population that collectively have an observable function. This method is simply to apply, achieves good results, is amenable to automation and can be easily modified to compensate for testing errors. M.A. Bishop is supported by AFOSR FA8750-06-C-0007. A.J. Macula is supported by NSF-0436298, AFOSR FA8750-06-C-0007.     

Testing Multiple Forecasters

We consider a cross‐calibration test of predictions by multiple potential experts in a stochastic environment. This test checks whether each expert is calibrated conditional on the predictions made by other experts. We show that this test is good in the sense that a true expert—one informed of the true distribution of the process—is guaranteed to pass the test no matter what the other potential experts do, and false experts will fail the test on all but a small (category I) set of true distributions. Furthermore, even when there is no true expert present, a test similar to cross‐calibration cannot be simultaneously manipulated by multiple false experts, but at the cost of failing some true experts.