Maximum likelihood estimation

Score (statistics)

In statistics, the score (or informant) is the gradient of the log-likelihood function with respect to the parameter vector. Evaluated at a particular point of the parameter vector, the score indicates the steepness of the log-likelihood function and thereby the sensitivity to infinitesimal changes to the parameter values. If the log-likelihood function is continuous over the parameter space, the score will vanish at a local maximum or minimum; this fact is used in maximum likelihood estimation to find the parameter values that maximize the likelihood function. Since the score is a function of the observations that are subject to sampling error, it lends itself to a test statistic known as score test in which the parameter is held at a particular value. Further, the ratio of two likelihood functions evaluated at two distinct parameter values can be understood as a definite integral of the score function. (Wikipedia).

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Asymptotic theory (statistics) | Statistics | Gradient | Chi-squared distribution | Probability density function | Continuous function | Standard score | Estimator | Fisher information | Parameter space | Score test | Statistical parameter | Bernoulli trial | Partial derivative | Information theory | Leibniz integral rule | Maxima and minima | Variance | Likelihood-ratio test | Sample space | Bernoulli process | Maximum likelihood estimation | Realization (probability) | Likelihood function | Sampling error | Likelihood ratio | Hessian matrix | Infinitesimal | Numerical analysis | Expected value | Natural logarithm | Statistic | Test statistic | Scoring algorithm