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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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Various properties of the regression vector produced by cyclic subspace regression with regard to the meancentered linear regression equation are put forth. In particular, the subspace associated with the creation of is shown to contain a basis that maximizes certain covariances with respect to , the orthogonal projection of onto a specific subspace of the range of X. This basis is constructed. Moreover, this paper shows how the maximum covariance values effect the . Several alternative representations of are also developed. These representations show that is a modified version of the l-factor principal components regression vector , with the modification occurring by a nonorthogonal projection. Additionally, these representations enable prediction properties associated with to be explicitly identified. Finally, methods for choosing factors are spelled out. 相似文献
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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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Consider a nonlinear partial spline model . This article studies the estimation problem of when g0 is approximated by some graduating function. Some asymptotic results for are derived. In particular, it is shown that can be estimated with the usual parametric convergence rate without undersmoothing g0. 相似文献
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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
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