关于重采样（resampling），也就是置换检验（permutation tests），有一本讲得很好的书（摘自我的 TeX 格式参考文献）：Sidney Siegel 所著的《Nonparametric Statistics for the Behavioral Sciences》，McGraw-Hill 出版，纽约，1956 年。\ \ 没错，50 多年前就已经有关于这类检验的好书了。也可以用独立同分布（i.i.d.）假设来证明它。但如果是一个更弱的……
There is a nice treatment of resampling, i.e., permutation tests, in (from my TeX format bibliography) Sidney Siegel, {\it Nonparametric Statistics for the Behavioral Sciences,\/} McGraw-Hill, New York, 1956.\ \ Right, there was already a good book on such tests over 50 years ago. Can also justify it with an independence, identically distributed assumption. But a weaker…
……有个假设检验。关于这方面的文献汗牛充栋，比如 E. L. Lehmann 的《Testing Statistical Hypotheses》，E. L. Lehmann 的《Nonparametrics: Statistical Methods Based on Ranks》，Sidney Siegel 的《Nonparametric Statistics for the Behavioral Sciences》。在这个场景下，PG 会对非参数（non-parametric）的情况更感兴趣，也就是分布无关（distribution-free），即我们不对概率分布做任何假设。我们进行假设检验都是先从一个假设开始……
…has an hypothesis test. There's a large literature for that, e.g., E. L. Lehmann, Testing Statistical Hypotheses. E. L. Lehmann, Nonparametrics: Statistical Methods Based on Ranks. Sidney Siegel, Nonparametric Statistics for the Behavioral Sciences. In this case, PG will be more interested in the non-parametric case, i.e., distribution-free where we make no assumptions about probability distributions. We start an hypothesis test with an hypothesis,…
第 2 版从没离开过我的书桌：Siegel, S., & Castellan, N. J. (1988). Nonparametric statistics for the behavioral sciences (2nd ed.) New York: McGraw-Hill.
The 2nd edition is never far from my desk: Siegel, S., & Castellan, N. J. (1988). Nonparametric statistics for the behavioral sciences (2nd ed.) New York: McGraw-Hill.
可以考虑下，比如说 Sidney Siegel 和 N. John Castellan, Jr. 的《Nonparametric Statistics for the Behavioral Sciences, Second Edition》，ISBN 0-07-057357-3，McGraw-Hill 出版，纽约，1988 年。所以，“非参数”意味着不对基于参数的概率分布做假设。或者，也可以叫这些内容为分布无关（distribution-free）……
Might consider, say, Sidney Siegel, N. John Castellan, Jr. 'Nonparametric Statistics for the Behavioral Sciences, Second Edition', ISBN 0-07-057357-3, McGraw-Hill, New York, 1988. So, "nonparametric" means make no assumptions about a probability distribution based on parameters. Or, call the material distribution-free.…
对于统计学习，我提到的那本《Nonparametric Statistics for the Behavioral Sciences》应该能对统计学习做出很好的贡献。其中一些技术非常健壮（robust），也就是说所需要的假设极其少，以至于在自动应用的 AI 中应该会特别受欢迎……
For statistical learning, the book I mentioned Nonparametric Statistics for the Behavioral Sciences, should make a good contribution to statistical learning. Some of the techniques are so robust, i.e., need such meager assumptions, that they should be especially welcome in automatically applied AI…
……进行检验啊，伙计们。抱歉了。想了解更多，可以看看一些经典著作：E. L. Lehmann 的《Testing Statistical Hypotheses》，E. L. Lehmann 的《Nonparametrics: Statistical Methods Based on Ranks》，Sidney Siegel 的《Nonparametric Statistics for the Behavioral Sciences》。有一次我向思科展示我的工作。他们的反应是我的成果“只是统计学而已”。额，你们到底期待啥啊？想要某种确定性的、非 0 即 1 的东西来判断健康还是生病？你们知道这意味着什么……
…testing, guys. Sorry 'bout that. For more, see, say some of the classics: E. L. Lehmann, Testing Statistical Hypotheses. E. L. Lehmann, Nonparametrics: Statistical Methods Based on Ranks. Sidney Siegel, Nonparametric Statistics for the Behavioral Sciences. Once I presented my work to Cisco. Their reaction was that my work was "just statistical". Well, what the heck do you expect? Want something deterministic, 0 or 1, for healthy or sick? Do you realize what…
关于重采样（resampling），也就是置换检验（permutation tests），有一本讲得很好的书（摘自我的 TeX 格式参考文献）：Sidney Siegel 所著的《Nonparametric Statistics for the Behavioral Sciences》，McGraw-Hill 出版，纽约，1956 年。\ \ 没错，50 多年前就已经有关于这类检验的好书了。也可以用独立同分布（i.i.d.）假设来证明它。但如果是一个更弱的……
There is a nice treatment of resampling, i.e., permutation tests, in (from my TeX format bibliography) Sidney Siegel, {\it Nonparametric Statistics for the Behavioral Sciences,\/} McGraw-Hill, New York, 1956.\ \ Right, there was already a good book on such tests over 50 years ago. Can also justify it with an independence, identically distributed assumption. But a weaker…
……有个假设检验。关于这方面的文献汗牛充栋，比如 E. L. Lehmann 的《Testing Statistical Hypotheses》，E. L. Lehmann 的《Nonparametrics: Statistical Methods Based on Ranks》，Sidney Siegel 的《Nonparametric Statistics for the Behavioral Sciences》。在这个场景下，PG 会对非参数（non-parametric）的情况更感兴趣，也就是分布无关（distribution-free），即我们不对概率分布做任何假设。我们进行假设检验都是先从一个假设开始……
…has an hypothesis test. There's a large literature for that, e.g., E. L. Lehmann, Testing Statistical Hypotheses. E. L. Lehmann, Nonparametrics: Statistical Methods Based on Ranks. Sidney Siegel, Nonparametric Statistics for the Behavioral Sciences. In this case, PG will be more interested in the non-parametric case, i.e., distribution-free where we make no assumptions about probability distributions. We start an hypothesis test with an hypothesis,…
第 2 版从没离开过我的书桌：Siegel, S., & Castellan, N. J. (1988). Nonparametric statistics for the behavioral sciences (2nd ed.) New York: McGraw-Hill.
The 2nd edition is never far from my desk: Siegel, S., & Castellan, N. J. (1988). Nonparametric statistics for the behavioral sciences (2nd ed.) New York: McGraw-Hill.
可以考虑下，比如说 Sidney Siegel 和 N. John Castellan, Jr. 的《Nonparametric Statistics for the Behavioral Sciences, Second Edition》，ISBN 0-07-057357-3，McGraw-Hill 出版，纽约，1988 年。所以，“非参数”意味着不对基于参数的概率分布做假设。或者，也可以叫这些内容为分布无关（distribution-free）……
Might consider, say, Sidney Siegel, N. John Castellan, Jr. 'Nonparametric Statistics for the Behavioral Sciences, Second Edition', ISBN 0-07-057357-3, McGraw-Hill, New York, 1988. So, "nonparametric" means make no assumptions about a probability distribution based on parameters. Or, call the material distribution-free.…
对于统计学习，我提到的那本《Nonparametric Statistics for the Behavioral Sciences》应该能对统计学习做出很好的贡献。其中一些技术非常健壮（robust），也就是说所需要的假设极其少，以至于在自动应用的 AI 中应该会特别受欢迎……
For statistical learning, the book I mentioned Nonparametric Statistics for the Behavioral Sciences, should make a good contribution to statistical learning. Some of the techniques are so robust, i.e., need such meager assumptions, that they should be especially welcome in automatically applied AI…
……进行检验啊，伙计们。抱歉了。想了解更多，可以看看一些经典著作：E. L. Lehmann 的《Testing Statistical Hypotheses》，E. L. Lehmann 的《Nonparametrics: Statistical Methods Based on Ranks》，Sidney Siegel 的《Nonparametric Statistics for the Behavioral Sciences》。有一次我向思科展示我的工作。他们的反应是我的成果“只是统计学而已”。额，你们到底期待啥啊？想要某种确定性的、非 0 即 1 的东西来判断健康还是生病？你们知道这意味着什么……
…testing, guys. Sorry 'bout that. For more, see, say some of the classics: E. L. Lehmann, Testing Statistical Hypotheses. E. L. Lehmann, Nonparametrics: Statistical Methods Based on Ranks. Sidney Siegel, Nonparametric Statistics for the Behavioral Sciences. Once I presented my work to Cisco. Their reaction was that my work was "just statistical". Well, what the heck do you expect? Want something deterministic, 0 or 1, for healthy or sick? Do you realize what…