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小伟 · 2020年02月16日

问一道题:NO.PZ2020010801000030

问题如下:

If you use a general-to-specific model selection with a test size of a, what is the probability that one or more irrelevant regressors are included when the regressors are uncorrelated?

选项:

解释:

If the regressors are uncorrelated, then their joint distribution has no correlation, and so the probability that one-or-more irrelevant regressors is included is 1 minus the probability that none are. The probability of including a single irrelevant regressor is 1α1 - \alpha, where a is the test size. This is the definition of the size of a test. The probability that no irrelevant regressors are included is (1α)p(1 - \alpha)^p, where p is the number of variables considered.

The probability that no irrelevant regressors are included is (1−α)p,这个是怎么求出来的,讲义的第几页

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1 个答案

品职答疑小助手雍 · 2020年02月17日

同学你好,这个就是相当于一个独立事件发生的概率是1-α,这件事发生p次的概率就是(1-α)的p次方。

没有无关的概率就是(1-α)^p, 那么至少有1个无关的regressors被包含的概率就是1-(1-a)^p ,这就是这题的完整答案。