集智百科 - 复杂系统|人工智能|复杂科学|复杂网络|自组织

更改

重尾分布 (查看源代码)

2021年2月26日 (五) 16:07的版本

删除1,994字节 、 2021年2月26日 (五) 16:07
→‎Estimation of heavy-tailed density 重尾密度的估计
第229行： 第229行：  
* 用于估计重尾指数的软件[http://www.cs.bu.edu/~crovella/aest.html aest]和C。<ref>{{Cite journal | last1 = Crovella | first1 = M. E. | last2 = Taqqu | first2 = M. S. | title = Estimating the Heavy Tail Index from Scaling Properties| journal = Methodology and Computing in Applied Probability | volume = 1 | pages = 55–79 | year = 1999 | doi = 10.1023/A:1010012224103 | url = http://www.cs.bu.edu/~crovella/paper-archive/aest.ps| pmid =  | pmc = }}</ref>
 
* 用于估计重尾指数的软件[http://www.cs.bu.edu/~crovella/aest.html aest]和C。<ref>{{Cite journal | last1 = Crovella | first1 = M. E. | last2 = Taqqu | first2 = M. S. | title = Estimating the Heavy Tail Index from Scaling Properties| journal = Methodology and Computing in Applied Probability | volume = 1 | pages = 55–79 | year = 1999 | doi = 10.1023/A:1010012224103 | url = http://www.cs.bu.edu/~crovella/paper-archive/aest.ps| pmid =  | pmc = }}</ref>
   −
== Estimation of heavy-tailed density 重尾密度的估计 ==
+
== 重尾密度的估计 ==
 +
 
   −
Nonparametric approaches to estimate heavy- and superheavy-tailed probability density functions were given in
  −
Markovich.<ref name="Markovich2007">{{cite book
  −
| author=Markovich N.M.
  −
| title=Nonparametric Analysis of Univariate Heavy-Tailed data: Research and Practice
  −
| year=2007
  −
| series=Chitester: Wiley
  −
| isbn=978-0-470-72359-3
  −
}}</ref> These are approaches based on variable bandwidth and long-tailed kernel estimators;  on the preliminary data transform to a new random variable at finite or infinite intervals which is more convenient for the estimation and then inverse transform of the obtained density estimate; and "piecing-together approach" which provides a certain parametric model for the tail of the density and a non-parametric model to approximate the mode of the density. Nonparametric estimators require an appropriate selection of tuning (smoothing) parameters like a bandwidth of kernel estimators and the bin width of the histogram. The well known data-driven methods of such selection are a cross-validation and its modifications,  methods based on the minimization of the mean squared error (MSE) and its asymptotic and their upper bounds.<ref name="WandJon1995">{{cite book
  −
| author=Wand M.P., Jones M.C.
  −
| title=Kernel smoothing
  −
| year=1995
  −
| series=New York: Chapman and Hall
  −
| isbn=978-0412552700
  −
}}</ref> A discrepancy method which uses well-known nonparametric statistics like Kolmogorov-Smirnov's, von Mises and Anderson-Darling's ones as a metric in the space of distribution functions (dfs) and quantiles of the later statistics as a known uncertainty or a discrepancy value can be found in.<ref name="Markovich2007"/> Bootstrap is another tool to find smoothing parameters using  approximations of unknown MSE by different schemes of re-samples selection, see e.g.<ref name="Hall1992">{{cite book
  −
| author=Hall P.
  −
| title=The Bootstrap and Edgeworth Expansion
  −
| year=1992
  −
| series=Springer
  −
| isbn=9780387945088
  −
}}</ref>
      
Markovich中给出了估计重尾和超重尾概率密度函数的非参数方法。<ref name="Markovich2007">{{cite book
 
Markovich中给出了估计重尾和超重尾概率密度函数的非参数方法。<ref name="Markovich2007">{{cite book
第271行： 第252行：  
| isbn=9780387945088
 
| isbn=9780387945088
 
}}</ref>
 
}}</ref>
−
  −
      
== See also 其他参考资料 ==
 
== See also 其他参考资料 ==
取自“https://wiki.swarma.org/index.php/特殊:移动版差异/21975”