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Quadratic minimisation problems in statistics 总被引:1,自引:0,他引:1
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Moritz Jirak 《Journal of multivariate analysis》2011,102(6):1032-1046
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Applications of quadratic minimisation problems in statistics 总被引:1,自引:0,他引:1
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Gérard Biau 《Journal of multivariate analysis》2005,94(1):196-208
Let f be an unknown multivariate density belonging to a prespecified parametric class of densities, , where k is unknown, but for all k and each has finite Vapnik-Chervonenkis dimension. Given an i.i.d. sample of size n drawn from f, we show that it is possible to select automatically, and without extra restrictions on f, an estimate with the property that . Our method is inspired by the combinatorial tools developed in Devroye and Lugosi (Combinatorial Methods in Density Estimation, Springer, New York, 2001) and it includes a wide range of density models, such as mixture models or exponential families. 相似文献