LIKELIHOOD RATIO TESTS 1 0 . 1 Likelihood Ratio Tests
LIKELIHOOD RATIO TESTS 1 0 . 1 Likelihood Ratio Tests
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似然比检验 1 0 。
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通讯作者：
Zhi
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作者：
Yingfei Dong;Changho Choi;Zhi
似然比检验是一种非常普遍的检验方法。设f（x; θ）是概率密度函数或概率分布，其中θ是在区间Θ中取值的真实的值参数，该区间Θ可以是整条真实的线。我们称Θ为参数空间。备择假设H1将参数θ限制到参数空间Θ的某个子集Θ 1。零假设H 0则是Θ 0相对于Θ的补数。例如，如果f（x; θ）是负指数分布，pdf f（x; θ）= 1 θ e −x/θ，x > 0，指定均值不等于3的备择假设有Θ = {θ：0 < θ < ∞}和Θ 1 = {θ：θ = 3}，因此Θ 0 = {θ：θ = 3}。首先，我们将讨论参数在零假设下完全指定的情况，因此对于参数空间中的某个值θ 0，H 0：θ = θ 0。也就是说，零假设是简单的，所以Θ 0 = {θ：θ = θ 0 }由单个点组成。
Likelihood ratio tests are a very general approach to testing. Let f (x; θ) be either a probability density function or a probability distribution where θ is a real valued parameter taking values in an interval Θ that could be the whole real line. We call Θ the parameter space. An alternative hypothesis H 1 will restrict the parameter θ to some subset Θ 1 of the parameter space Θ. The null hypothesis H 0 is then the complement of Θ 0 with respect to Θ. For instance, if f (x; θ) is the negative exponential distribution with pdf f (x; θ) = 1 θ e −x/θ for x > 0 the alternative hypothesis that specifies that the mean is not equal to 3 has Θ = {θ : 0 < θ < ∞} and Θ 1 = {θ : θ = 3} so Θ 0 = {θ : θ = 3}. Initially, we will confine our discussion to cases where the parameter is completely specified under the null hypothesis so H 0 : θ = θ 0 for some value θ 0 in the parameter space. That is, the null hypothesis is simple so Θ 0 = {θ : θ = θ 0 } consists of a single point.