Then suppose that a classification of a space is

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Then Suppose that a classification of a space is given: . Hence whenever and . The discriminant rule is usually the following form: if belongs to , We use denoting the cost where the sample coming from but was wrongly sent to , and the probability of this misjudgment is ( ) i f x 1,..., i r 1 2 , ,..., r q q q 1 2 1. r q q q n R 1 2 { , ,..., } r D D D D i j D D   i j 1 2 n r R D D D  i x G x i D 1,2,..., . i r ( | ) L j i i G j G ( | ) ( ) j i D p j i f x dx
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江西财经大学 统计学院 Introduce The Principle Let . Thus the ECM (expected cost of misclassification) caused by the above discriminant is: The Bayes discriminant analysis is to find a classification of such that ECM is minimum. For more Bayes discriminant analysis properties and detailed mathematical proofs refer to [1,2,3]. ( | ) 0 L i i 1 1 1 ( ,..., ) ( | ) ( | ) r r r i i j ECM D D q L j i P j i   n R
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江西财经大学 统计学院 10.5 Stepwise discriminant analysis The idea of Stepwise discriminant analysis The procedures of undertaking stepwise discriminant analysis in SPSS
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江西财经大学 统计学院 逐步判别法 ( 仅仅是在前面的方法中加入变量选择的功能 ) 有时,一些变量对于判别并没有什么作用,为了得到对判别最合 适的变量,可以使用逐步判别。即,一边判别,一边选择判别能 力最强的变量, 这个过程可以有进有出。一个变量的判别能力的判断方法有很多 种,主要利用各种检验,例如 Wilks Lambda 、Rao’s V The Squared Mahalanobis Distance Smallest F ratio The Sum of Unexplained Variations 等检验。其细节这里就不赘述 了;这些不同方法可由统计软件的各种选项来实现。逐步判别的 其他方面和前面的无异。
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江西财经大学 统计学院 2017/10/30 71 逐步判别 在多元回归中熟知,变量选择的好坏直接影响回归的效果, 而在判别分析中也有类似的问题。如果在某个判别问题中, 将其中最主要的指标忽略了,由此建立的判别函数其效果一 定不好。但是在许多问题中,事先并不十分清楚哪些指标是 主要的,这时,是否将有关的指标尽量收集加入计算才好呢? 理论和实践证明,指标太多了,不仅带来大量的计算,同时 许多对判别无作用的指标反而会干扰了我们的视线。因此适 当筛选变量的问题就成为一个很重要的事情。 凡具有筛选变量能力的判别方法统称为逐步判别法。和通常 的判别分析一样,逐步判别也有许多不同的原则,从而产生 各种方法。有关逐步判别法的理论基础详见 [1] 所讨论指标 的附加信息检验。
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江西财经大学 统计学院 The idea of Stepwise discriminant analysis Stepwise discriminant analysis is an attempt to find the best set of predictors. It is often used in an exploratory situation to identify those variables from among a larger number that might be used later in a more rigorous theoretically driven study.
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