概率测度的收敛

Hacker News 上怎么说

• HilbertSpace · 2009 年

  …0-12-079240-0, Academic Press, New York.\ \ Robert J.\ Serfling, {\it Approximation Theorems of Mathematical Statistics,\/} ISBN 0-471-02403-1, John Wiley and Sons, New York.\ \ P.\ Billingsley, {\it Convergence of Probability Measures, 2\raise0.5ex\hbox{ed},\/} ISBN: 0-471-19745-9, John Wiley, New York.\ \ R.\ S.\ Lipster and A.\ N.\ Shiryayev, {\it Statistics of Random Processes I, II,} ISBN 0-387-90226-0, Springer-Verlag, New York.\…

  …0-12-079240-0, Academic Press, New York.\ \ Robert J.\ Serfling, {\it Approximation Theorems of Mathematical Statistics,\/} ISBN 0-471-02403-1, John Wiley and Sons, New York.\ \ P.\ Billingsley, {\it Convergence of Probability Measures, 2\raise0.5ex\hbox{ed},\/} ISBN: 0-471-19745-9, John Wiley, New York.\ \ R.\ S.\ Lipster and A.\ N.\ Shiryayev, {\it Statistics of Random Processes I, II,} ISBN 0-387-90226-0, Springer-Verlag, New York.\…

• graycat · 2015 年

  …搭档自己就能找出那个笔误。要是有人想试试，就在这儿回复，我会发论文的 PDF。提示：最好能觉得比如 Patrick Billingsley 的《Convergence of Probability Measures》读起来既有趣又轻松，而要做到这一点，你起码得非常享受 Walter Rudin 的《Real and Complex Analysis》前半部分（实分析部分）以及 Walter Rudin 的《Principles of Mathematical Analysis》……

  …partner on their own can find the typo. Should such a person wish to try, then reply here, and I will send a PDF of the paper. Hint: It would be good to be able to find, say, Patrick Billingsley, 'Convergence of Probability Measures' fun and easy reading, and for that should have greatly enjoyed, say, at least the first (real) half of Walter Rudin, 'Real and Complex Analysis' and Walter Rudin, 'Principles of Mathematical Analysis'.…

• graycat · 2014 年

  …在斯坦福的讲座。长期以来，我们对理论统计学和应用统计学以及如何运用它们已经了解得非常透彻了。统计学里优秀的成果都是高质量的纯数/应用数学，比如 Billingsley 的《Convergence of Probability Measures》，里面有被 Le Cam 称为“tightness”（紧性）的 Ulam 定理；还有 Brillinger 关于时间序列的工作、Serfling 关于极限理论的成果、Rao 关于线性方法的研究、Breiman 关于 CART 的成果等等。而在……里面我看不到同等水准的质量

  …lectures at Stanford. We've known a lot about pure and applied statistics and how to use them for a very long time. The good work in statistics is high quality pure/applied math, e.g., Billingsly, 'Convergence of Probability Measures', e.g. with Ulam's result Le Cam called 'tightness', Brillinger on time series, Serfling on limit theorems, Rao on linear methods, Breiman on CART, and much more. I'm not seeing comparable quality in…

• graycat · 2018 年

  …检验的显著性，并用了 S. Ulam 一个被 LeCam 称为“tightness”的经典结论，来证明该检验的功效优于平凡检验。Ulam 的这个结论收录在 P. Billingsley 的《Convergence of Probability Measures》里。Billingsley 长期任教于芝加哥大学。

  …significance of the test, and used a classic result, LeCam called "tightness" of S. Ulam to show that the power of the test was better than that of a trivial test. Ulam's result is in P. Billingsley, Convergence of Probability Measures. Billingsley was long at U. Chicago.

• ten_fingers · 2012 年

  …尝试，他的第一项贡献产出了大约1.5万吨。在此之前，他在概率论领域搞出了一个很棒的成果，被法国概率学家 Le Cam 称为“tightness”，在 Billingsley 的《Convergence of Probability Measures》中有很精彩的阐述。(2) 研究方面，我确实相信 VC 们收不到多少基于前沿研究的有前途的商业提案。原因之一是有才华、受过良好训练的研究人员转型去创业的并不多。…

  …try, his first contribution yielded about 15 thousand tons. Before that he had a nice result in probability the French probabilist Le Cam called 'tightness' with a nice presentation in Billingsley's 'Convergence of Probability Measures'. (2) The Research I can believe that the VCs don't receive many promising proposals based on research. One reason is that not many talented, well trained researchers cross over to become entrepreneurs.…

• graycat · 2013 年

  …距离原点大于 r 的概率质量小于 h。这个结论在相当一般的空间中都成立，不过我现在得去查查细节了。细节在 P. Billingsley 1999 年的《Convergence of Probability Measures》里。我曾经在一篇论文里用过这个结论。这是个很棒的结论，在概率论的高等研究中偶尔会用到。

  …that the probability mass farther than r from the origin is less than h. This result holds in spaces of considerable generality, but I'd have to look up the details now. Details are in P. Billingsley, 'Convergence of Probability Measures', 1999. I used the result in a paper once. It's nice result and gets used occasionally in advanced work in probability.

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