Large deviations theory | Information theory | Statistical hypothesis testing

Error exponents in hypothesis testing

In statistical hypothesis testing, the error exponent of a hypothesis testing procedure is the rate at which the probabilities of Type I and Type II decay exponentially with the size of the sample used in the test. For example, if the probability of error of a test decays as , where is the sample size, the error exponent is . Formally, the error exponent of a test is defined as the limiting value of the ratio of the negative logarithm of the error probability to the sample size for large sample sizes: . Error exponents for different hypothesis tests are computed using Sanov's theorem and other results from large deviations theory. (Wikipedia).

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Related pages

Large deviations theory | Kullback–Leibler divergence | Likelihood-ratio test | Type I and type II errors | False positives and false negatives | Sanov's theorem | Probability density function | Statistical hypothesis testing | Independent and identically distributed random variables