Score test: Difference between revisions
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The ''score test'' is a statistical test of a simple [[null hypothesis]] (that the parameter of interest <math>\theta</math> is |
The '''score test''' is a statistical test of a simple [[null hypothesis]] (that the parameter of interest <math>\theta</math> is |
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equal to some particular value <math>\theta_0</math>): |
equal to some particular value <math>\theta_0</math>): |
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:<math> |
:<math> |
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and identifying the <math>C</math> above with <math>\log(K)</math>. |
and identifying the <math>C</math> above with <math>\log(K)</math>. |
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==See |
==See also== |
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*[[Fisher information]] |
*[[Fisher information]] |
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*[[Uniformly |
*[[Uniformly most powerful test]] |
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*[[Wald |
*[[Wald test]] |
Revision as of 21:11, 26 May 2005
The score test is a statistical test of a simple null hypothesis (that the parameter of interest is equal to some particular value ):
Where is the likelihood function, is the value of the parameter of interest under the null hypothesis, and is a constant set depending on the size of the test desired (i.e. the probability of rejecting if is true; see Type I error).
The score test is the most powerful test for small deviations from . To see this, consider testing versus . By the Neyman-Pearson lemma, the most powerful test has the form
Taking the log of both sides yields
The score test follows making the substitution
and identifying the above with .