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We find closed formulas for arbitrarily high mixed moments of characteristic polynomials of the Alternative Circular Unitary Ensemble, as well as closed formulas for the averages of ratios of characteristic polynomials in this ensemble. A comparison is made to analogous results for the Circular Unitary Ensemble. Both moments and ratios are studied via symmetric function theory and a general formula of Borodin-Olshanski-Strahov. [ABSTRACT FROM AUTHOR]

The authors consider the problem of recognition of a class of objects by the results of multispectral measurements (spectral brightness of signals) and available spectral and statistical characteristics of the given classes. On the basis of probabilistic and statistical considerations, as well as quantization of continuous distributions, the heuristic recognition criterion is proposed. Based on the criterion, the heuristic method of recognition is presented. Modifications of the method are proposed to improve its reliability and efficiency. [ABSTRACT FROM AUTHOR]

Let be a -dimensional normal distribution. Testing equal to a given matrix or equal to a given pair through the likelihood ratio test (LRT) is a classical problem in the multivariate analysis. When the population dimension is fixed, it is known that the LRT statistics go to -distributions. When is large, simulation shows that the approximations are far from accurate. For the two LRT statistics, in the high-dimensional cases, we obtain their central limit theorems under a big class of alternative hypotheses. In particular, the alternative hypotheses are not local ones. We do not need the assumption that and are proportional to each other. The condition suffices in our results. [ABSTRACT FROM AUTHOR]

This paper proposes a statistical framework for establishing prima facie evidence in WTO proceedings in which empirical evidence and statistical analysis play an important role. As our main contribution, we suggest a general guideline for the choice of the significance level in a statistical analysis, in order to meet the requirements for establishing prima facie evidence of a claim. We consider a fundamental asymmetry between whether a complainant’s initial claim is positive or negative. Statistically, a positive claim is one in favour of the alternative hypothesis, whereas a negative claim is one in favour of the null hypothesis. To account for this asymmetry, we suggest using different significance levels for positive and negative assertions, respectively. For positive claims, we suggest using the most commonly applied significance level of 5%. For negative claims, we suggest the less strict (but still commonly accepted) significance level of 10%. Choosing a less strict significance level in the case of a negative claim than in the case of a positive claim accounts for another fundamental asymmetry between the two possible outcomes of a statistical hypothesis test: rejecting the null hypothesis or not. Our framework helps to define reasonable hurdles in WTO proceedings to substantiate claims using statistical methods while leaving enough leeway for the panel and the Appellant Body to make adjustments on a case-by-case basis. [ABSTRACT FROM PUBLISHER]

We consider inference on a scalar parameter of interest in the presence of a nuisance parameter, using a likelihood-based statistic which is asymptotically normally distributed under the null hypothesis. Higher-order expansions are used to compare the repeated sampling distribution, under a general contiguous alternative hypothesis, of p-values calculated from the asymptotic normal approximation to the null sampling distribution of the statistic with the distribution of p-values calculated by bootstrap approximations. The results of comparisons in terms of power of different testing procedures under an alternative hypothesis are closely related to differences under the null hypothesis, specifically the extent to which testing procedures are conservative or liberal under the null. Empirical examples are given which demonstrate that higher-order asymptotic effects may be seen clearly in small-sample contexts. [ABSTRACT FROM AUTHOR]

In this paper, a new sparse representation-based binary hypothesis (SRBBH) model for hyperspectral target detection is proposed. The proposed approach relies on the binary hypothesis model of an unknown sample induced by sparse representation. The sample can be sparsely represented by the training samples from the background-only dictionary under the null hypothesis and the training samples from the target and background dictionary under the alternative hypothesis. The sparse vectors in the model can be recovered by a greedy algorithm, and the same sparsity levels are employed for both hypotheses. Thus, the recovery process leads to a competition between the background-only subspace and the target and background subspace, which are directly represented by the different hypotheses. The detection decision can be made by comparing the reconstruction residuals under the different hypotheses. Extensive experiments were carried out on hyperspectral images, which reveal that the SRBBH model shows an outstanding detection performance. [ABSTRACT FROM PUBLISHER]

Previous research has found no consistent relationship between measures of disconfirmatory evidence, alternative hypotheses, and people's success in rule-discovery tasks. The present paper explores falsification's inductive benefit under the 'context of discovery' in Wason's 2-4-6 task by developing a new type of alternative hypothesis, which we label the 'new-perspective hypothesis'. Experiment 1 found that falsification is effective only when a new-perspective hypothesis is generated, rather than a same-perspective hypothesis. The total number of alternative hypotheses was also unrelated to rule-discovery success. Experiment 2 replicated Experiment 1 but included the addition of a different name-content task as well as two levels of task difficulty. The main findings were similar to those for Experiment 1, and the new-perspective hypothesis was observed to be most important for the difficult rule-discovery task. These results help to clarify the important ways new-perspective hypotheses and disconfirmatory evidence contribute to successful rule-discovery performance. [ABSTRACT FROM AUTHOR]

Statistical methods have been broadly used to draw helpful information for various real applications in social science and engineering. Today, students are advised to have a good understanding on Statistics and be familiar with using statistical methods. However, most students in Business School or Liberal Arts School in Taiwan often feel intractable in learning statistical methods because of their weak basis of Mathematics. In this paper, I share my experience on teaching Statistics and illustrate some good explanations to statistical formulas based on practice viewpoints. An example regarding the quality assurance of smart cards is used to explain how to develop an asymptotic acceptance sampling plan according to the real operation conditions. A numerical study is conducted to discuss the merit and shortcoming of using censoring schemes. The estimation performance of maximum likelihood for various types of data is evaluated in terms of the bias and mean squared error through the aids of statistical software. These are useful to enhance students' interest in learning Statistics and make learning Statistics be more interesting and realistic to students in class. [ABSTRACT FROM AUTHOR]

A fundamental statistical problem is to indicate which of two hypotheses is better supported by the data. Statistics designed for this purpose are called weight of evidence. In this paper we study the problem of robust weights of evidence, optimal in their performance while robust in the infinitesimal sense of the influence function. [ABSTRACT FROM AUTHOR]

Research has shown that the judged probability of an event depends on the specificity with which the focal and alternative hypotheses are described. In particular, unpacking the components of the focal hypothesis generally increases the judged probability of the focal hypothesis, while unpacking the components of the alternative hypothesis decreases the judged probability of the focal hypothesis. As a consequence, the Judged probability of the union of disjoint events is generally less than the sum of their judged probabilities. This article shows that the total judged probability of a set of mutually exclusive and exhaustive hypotheses increases with the degree to which the evidence is compatible with these hypotheses. This phenomenon, which we refer to as the enhancement effect, is consistent with a descriptive account of subjective probability called support theory. [ABSTRACT FROM AUTHOR]

A class of alternative hypotheses to independence is proposed for two-way contingency tables. It is assumed that a certain proportion of the cell probabilities under independence has been removed from (or put into) each of a subset of cells and redistributed over (or taken from) the remaining cells, keeping the marginals unchanged. The redistribution or depletion is not necessarily restricted to neighboring cells. The proposed alternatives can be expressed in loglinear form amenable to usual methods of analyses. Two numerical examples are given. Some generalizations for two-way and multi-way tables are discussed. [ABSTRACT FROM AUTHOR]