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  2. Ratio test - Wikipedia

    en.wikipedia.org/wiki/Ratio_test

    In this example, the ratio of adjacent terms in the blue sequence converges to L=1/2. We choose r = (L+1)/2 = 3/4. Then the blue sequence is dominated by the red sequence r k for all n ≥ 2. The red sequence converges, so the blue sequence does as well. Below is a proof of the validity of the generalized ratio test.

  3. Sequential probability ratio test - Wikipedia

    en.wikipedia.org/wiki/Sequential_probability...

    The sequential probability ratio test (SPRT) is a specific sequential hypothesis test, developed by Abraham Wald [1] and later proven to be optimal by Wald and Jacob Wolfowitz. [2] Neyman and Pearson's 1933 result inspired Wald to reformulate it as a sequential analysis problem.

  4. Convergence tests - Wikipedia

    en.wikipedia.org/wiki/Convergence_tests

    If r = 1, the root test is inconclusive, and the series may converge or diverge. The root test is stronger than the ratio test: whenever the ratio test determines the convergence or divergence of an infinite series, the root test does too, but not conversely. [1]

  5. Ratio estimator - Wikipedia

    en.wikipedia.org/wiki/Ratio_estimator

    The ratio estimates are asymmetrical and symmetrical tests such as the t test should not be used to generate confidence intervals. The bias is of the order O(1/n) (see big O notation) so as the sample size (n) increases, the bias will asymptotically approach 0. Therefore, the estimator is approximately unbiased for large sample sizes.

  6. Neyman–Pearson lemma - Wikipedia

    en.wikipedia.org/wiki/Neyman–Pearson_lemma

    In practice, the likelihood ratio is often used directly to construct tests — see likelihood-ratio test.However it can also be used to suggest particular test-statistics that might be of interest or to suggest simplified tests — for this, one considers algebraic manipulation of the ratio to see if there are key statistics in it related to the size of the ratio (i.e. whether a large ...

  7. Multiple comparisons problem - Wikipedia

    en.wikipedia.org/wiki/Multiple_comparisons_problem

    For example, if one test is performed at the 5% level and the corresponding null hypothesis is true, there is only a 5% risk of incorrectly rejecting the null hypothesis. However, if 100 tests are each conducted at the 5% level and all corresponding null hypotheses are true, the expected number of incorrect rejections (also known as false ...

  8. Likelihood-ratio test - Wikipedia

    en.wikipedia.org/wiki/Likelihood-ratio_test

    The likelihood-ratio test, also known as Wilks test, [2] is the oldest of the three classical approaches to hypothesis testing, together with the Lagrange multiplier test and the Wald test. [3] In fact, the latter two can be conceptualized as approximations to the likelihood-ratio test, and are asymptotically equivalent.

  9. Monotone likelihood ratio - Wikipedia

    en.wikipedia.org/wiki/Monotone_likelihood_ratio

    The ratio of the density functions above is monotone in the parameter , so satisfies the monotone likelihood ratio property. In statistics , the monotone likelihood ratio property is a property of the ratio of two probability density functions (PDFs).

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