In teaching the development of uniformly most powerful unbiased (UMPU) tests, one rarely discusses the performance of alternative biased tests. It is shown, through the comparison of two independent Bernoulli proportions, that a biased test (the Z test) can be more powerful than the UMPU test (Fisher's exact test—randomized) in a large region of the alternative parameter space. A more general example is also given. 相似文献
Standard resulrs on the extrema of quotients of quadratic forms are extended to the non-negative definite case. The maximum and the set over which it is achieved are characterized explicitly both in terms of generalized inverse matrices and generalized eigenvalues. These results become the basis of Scheffe type multiple comparisons in the usual way. To demonstrate their application to statistics with singular covariance matrices, the method is detailed for Mantel-Haenszel, Breslow, and Cox statistics. An example is presented illustrating a situation where the proposed Scheffe type comparisons may be better than the pairwise method. 相似文献
There are two common methods for statistical inference on 2 × 2 contingency tables. One is the widely taught Pearson chi-square test, which uses the well-known χ2statistic. The chi-square test is appropriate for large sample inference, and it is equivalent to the Z-test that uses the difference between the two sample proportions for the 2 × 2 case. Another method is Fisher’s exact test, which evaluates the likelihood of each table with the same marginal totals. This article mathematically justifies that these two methods for determining extreme do not completely agree with each other. Our analysis obtains one-sided and two-sided conditions under which a disagreement in determining extreme between the two tests could occur. We also address the question whether or not their discrepancy in determining extreme would make them draw different conclusions when testing homogeneity or independence. Our examination of the two tests casts light on which test should be trusted when the two tests draw different conclusions. 相似文献
Although the noncentral hypergeometric distribution underlies conditional inference for 2 × 2 tables, major statistical packages lack support for this distribution. This article introduces fast and stable algorithms for computing the noncentral hypergeometric distribution and for sampling from it. The algorithms avoid the expensive and explosive combinatorial numbers by using a recursive relation. The algorithms also take advantage of the sharp concentration of the distribution around its mode to save computing time. A modified inverse method substantially reduces the number of searches in generating a random deviate. The algorithms are implemented in a Java class, Hypergeometric, available on the World Wide Web. 相似文献
Multi-criteria inventory classification groups inventory items into classes, each of which is managed by a specific re-order policy according to its priority. However, the tasks of inventory classification and control are not carried out jointly if the classification criteria and the classification approach are not robustly established from an inventory-cost perspective. Exhaustive simulations at the single item level of the inventory system would directly solve this issue by searching for the best re-order policy per item, thus achieving the subsequent optimal classification without resorting to any multi-criteria classification method. However, this would be very time-consuming in real settings, where a large number of items need to be managed simultaneously.
In this article, a reduction in simulation effort is achieved by extracting from the population of items a sample on which to perform an exhaustive search of best re-order policies per item; the lowest cost classification of in-sample items is, therefore, achieved. Then, in line with the increasing need for ICT tools in the production management of Industry 4.0 systems, supervised classifiers from the machine learning research field (i.e. support vector machines with a Gaussian kernel and deep neural networks) are trained on these in-sample items to learn to classify the out-of-sample items solely based on the values they show on the features (i.e. classification criteria). The inventory system adopted here is suitable for intermittent demands, but it may also suit non-intermittent demands, thus providing great flexibility. The experimental analysis of two large datasets showed an excellent accuracy, which suggests that machine learning classifiers could be implemented in advanced inventory classification systems. 相似文献