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Bernhard G. Bodmann Martin Ehler Manuel Gräf 《Journal of Theoretical Probability》2018,31(4):2167-2193
We aim to compute the first few moments of a high-dimensional random vector from the first few moments of a number of its low-dimensional projections. To this end, we identify algebraic conditions on the set of low-dimensional projectors that yield explicit reconstruction formulas. We also provide a computational framework, with which suitable projectors can be derived by solving an optimization problem. Finally, we show that randomized projections permit approximate recovery. 相似文献
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Two-parameter gamma distributions are widely used in liability theory, lifetime data analysis, financial statistics, and other areas. Finite mixtures of gamma distributions are their natural extensions, and they are particularly useful when the population is suspected of heterogeneity. These distributions are successfully employed in various applications, but many researchers falsely believe that the maximum likelihood estimator of the mixing distribution is consistent. Similarly to finite mixtures of normal distributions, the likelihood function under finite gamma mixtures is unbounded. Because of this, each observed value leads to a global maximum that is irrelevant to the true distribution. We apply a seemingly negligible penalty to the likelihood according to the shape parameters in the fitted model. We show that this penalty restores the consistency of the likelihoodbased estimator of the mixing distribution under finite gamma mixture models. We present simulation results to validate the consistency conclusion, and we give an example to illustrate the key points. 相似文献
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This study is aimed at proposing a practical green procedure for the synthesis of octahydroquinazolinone derivatives using benzaldehyde, dimedone and urea under microwave irradiation in water. A surfactant type polyoxometalate-based organic–inorganic hybrid was able to efficiently catalyze this synthesis. The catalyst was prepared and characterized by Fourier transform infrared, UV–Vis, X-ray diffraction, and thermogravimetric analysis. The employed catalyst exerted a synergistic effect; the anion part acted as a catalyst while the cation part acted as a surfactant in order to increase the concentration of organic reactants in water. The main advantage of this method is its remarkable yield in short reaction periods, which results in the rendering of products with high purity. Moreover, this heterocatalyst is capable of being easily recovered and reused several times. The influences of reaction conditions were studied systematically, and a possible catalysis mechanism was proposed for understanding the highly efficient heterogeneous catalytic behavior. 相似文献