二次Logistic判别分析及其气象应用
QUADRATIC LOGISTIC DISCRIMINANT ANALYSIS AND ITS APPLICATIONS IN METEOROLOGY
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摘要: 在线性Logistic判别中,各母体的相关结构是相同的,但对理论研究和实际应用都很重要的是各母体的相关结构不相同的情况,这样就引出了二次Logistic判别的问题。若变量维数p不太小,如P4,则在完全Logistic判别中将出现太多的要计算的参数。利用拟牛顿迭代法解出由最大似然估计所得到的关于Logistic参数的超越方程组。并作出华北地区夏季旱涝预报的二次Logistic判别分析,以及北京7月上旬内最高气温大于35℃的日数不少于2d与少于2d的二次Logistic判别分析的实例。最后,还提出了在某些特殊情况下的近似方法。Abstract: In the linear logistic discrimination, the dependence structures of various populations are the same. But it is important for theoretical researchs and practical applications that the dependence structures are different in various populations, thus the quadratic discrimination is produced in the paper. The full quadratic logistic discriminant approach has too many parameters to be estimated if the dimensionality, p, is not small, say p>4.An approximation is suggested here which gives a quadratic term in the discriminant function but with a greatly reduced number of parameters. A quasi-Newton iterative computation is used to solve the equations from maximum likelihood estimation. Examples of the prediction of the drought or flood in North China, and in which the number of days when the most high temperature 35℃ in the 1st decade of July in Beijing is less than 2 or not, are provided. Other approximations are suggested in some special cases.
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