| 書目名稱 | Projecting Statistical Functionals | | 編輯 | Tomasz Rychlik | | 視頻video | http://file.papertrans.cn/761/760909/760909.mp4 | | 叢書名稱 | Lecture Notes in Statistics | | 圖書封面 |  | | 描述 | About 10 years ago I began studying evaluations of distributions of or- der statistics from samples with general dependence structure. Analyzing in [78] deterministic inequalities for arbitrary linear combinations of order statistics expressed in terms of sample moments, I observed that we obtain the optimal bounds once we replace the vectors of original coefficients of the linear combinations by the respective Euclidean norm projections onto the convex cone of vectors with nondecreasing coordinates. I further veri- fied that various optimal evaluations of order and record statistics, derived earlier by use of diverse techniques, may be expressed by means of projec- tions. In Gajek and Rychlik [32], we formulated for the first time an idea of applying projections onto convex cones for determining accurate moment bounds on the expectations of order statistics. Also for the first time, we presented such evaluations for non parametric families of distributions dif- ferent from families of arbitrary, symmetric, and nonnegative distributions. We realized that this approach makes it possible to evaluate various func- tionals of great importance in applied probability and statistics in di | | 出版日期 | Book 2001 | | 關鍵詞 | Variance; average; probability; statistics | | 版次 | 1 | | doi | https://doi.org/10.1007/978-1-4612-2094-7 | | isbn_softcover | 978-0-387-95239-0 | | isbn_ebook | 978-1-4612-2094-7Series ISSN 0930-0325 Series E-ISSN 2197-7186 | | issn_series | 0930-0325 | | copyright | Springer-Verlag New York, Inc. 2001 |
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