Call
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 P e r r o r {\displaystyle P_{\mathrm {error} }} of a test decays as e − n β {\displaystyle e^{-n\beta }} , where n {\displaystyle n} is the sample size, the error exponent is β {\displaystyle \beta }.
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: lim n → ∞ − ln P error n {\displaystyle \lim _{n\to \infty }{\frac {-\ln P_{\text{error}}}{n}}}. Error exponents for different hypothesis tests are computed using Sanov's theorem and other results from large deviations theory.
Talk Doctor Online in Bissoy App