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Deviations of power quality indices (PQI) from standard values in power supply systems of industrial consumers lead to defective products, complete shutdown of production processes, and significant damage. At the same time, the PQI requirements vary depending on the industrial consumer, which is due to different kinds, types, and composition of essential electrical loads. To ensure their reliable operation, it is crucial to introduce automatic PQI control devices, which evaluate the extent of distortion of the sinusoidal voltage waveform of a three-phase system. This allows the power dispatchers of grid companies and industrial enterprises to quickly make decisions on the measures to be taken in external and internal power supply networks to ensure that the PQI values are within the acceptable range. This paper proposes the use of an integrated indicator to assess the extent of distortion of the sinusoidal voltage waveform in a three-phase system. This indicator is based on the use of the magnitude of the ratio of complex amplitudes of the forward and reverse rotation of the space vector. In the study discussed, block diagrams of algorithms and flowcharts of automatic PQI control devices are developed, which implement parametric and nonparametric multiple-hypothesis sequential analysis using an integrated indicator. In this case, Palmer’s algorithm and the nearest neighbor method are used. The calculations demonstrate that the developed algorithms have high speed and high performance in detecting deviations of the electrical power quality.

We consider a multiple‐hypothesis testing setting where the hypotheses are ordered and one is only permitted to reject an initial contiguous block H1,…,Hk of hypotheses. A rejection rule in this setting amounts to a procedure for choosing the stopping point k. This setting is inspired by the sequential nature of many model selection problems, where choosing a stopping point or a model is equivalent to rejecting all hypotheses up to that point and none thereafter. We propose two new testing procedures and prove that they control the false discovery rate in the ordered testing setting. We also show how the methods can be applied to model selection by using recent results on p‐values in sequential model selection settings.

Under mild Markov assumptions, sufficient conditions for strict minimax optimality of sequential tests for multiple hypotheses under distributional uncertainty are derived. First, the design of optimal sequential tests for simple hypotheses is revisited, and it is shown that the partial derivatives of the corresponding cost function are closely related to the performance metrics of the underlying sequential test. Second, an implicit characterization of the least favorable distributions for a given testing policy is stated. By combining the results on optimal sequential tests and least favorable distributions, sufficient conditions for a sequential test to be minimax optimal under general distributional uncertainties are obtained. The cost function of the minimax optimal test is further identified as a generalized f-dissimilarity and the least favorable distributions as those that are most similar with respect to this dissimilarity. Numerical examples for minimax optimal sequential tests under different uncertainties illustrate the theoretical results.

Testing of multiple hypotheses involves statistics that are strongly dependent in some applications, but most work on this subject is based on the assumption of independence. We propose a new method for estimating the false discovery rate of multiple hypothesis tests, in which the density of test scores is estimated parametrically by minimizing the Kullback-Leibler distance between the unknown density and its estimator using the stochastic approximation algorithm, and the false discovery rate is estimated using the ensemble averaging method. Our method is applicable under general dependence between test statistics. Numerical comparisons between our method and several competitors, conducted on simulated and real data examples, show that our method achieves more accurate control of the false discovery rate in almost all scenarios.

This paper considers some methods for reducing the number of significance tests undertaken when analyzing and reporting results of clinical trials. Emphasis is placed on designing and analyzing clinical trials to examine a composite hypothesis concerning multiple endpoints and combining this multiple endpoint methodology with group sequential methodology. Four methods for composite hypotheses are considered: an ordinary least squares and a generalized least squares approach both due to O'Brien (1984, Biometrics 40, 1079-1087), a new modification of these, and an approximate likelihood ratio test, due to Tang, Gnecco, and Geller (1989, Biometrika 76, 577-583). These are extended for group sequential use. In particular, simulation is used to generate critical values and sequences of nominal significance levels for the approximate likelihood ratio test, which is not normally distributed. An example is given and the relative merits of the suggested approaches are discussed.