# Score (statistics)

**scorescore functionscoringscore equationscoresscoring system**

In statistics, the score (or informant) is the gradient of the log-likelihood function with respect to the parameter vector.wikipedia

62 Related Articles

### Score test

**Lagrange multiplier testLagrange multiplierLagrange multiplier (LM) test**

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.

In statistics, the score test assesses constraints on statistical parameters based on the gradient of the likelihood function—known as the score—evaluated at the hypothesized parameter value under the null hypothesis.

### Fisher information

**Fisher information matrixinformation matrixinformation**

:The latter is known as the Fisher information and is written.

Formally, it is the variance of the score, or the expected value of the observed information.

### Likelihood function

**likelihoodlikelihood ratiolog-likelihood**

In statistics, the score (or informant) is the gradient of the log-likelihood function with respect to the parameter vector. Further, the ratio of two likelihood functions evaluated at two distinct parameter values can be understood as a definite integral of the score function. The score is the gradient (the vector of partial derivatives) of, the natural logarithm of the likelihood function, with respect to an m -dimensional parameter vector \theta.

This ensures that the score has a finite variance.

### Maximum likelihood estimation

**maximum likelihoodmaximum likelihood estimatormaximum likelihood estimate**

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.

where is the score and is the inverse of the Hessian matrix of the log-likelihood function, both evaluated the r th iteration.

### Support curve

The function being plotted is used in the computation of the score and Fisher information, and the graph has a direct interpretation in the context of maximum likelihood estimation and likelihood-ratio tests.

### Scoring algorithm

**Fisher scoringFisher's scoringFisher scoring algorithm**

First, suppose we have a starting point for our algorithm \theta_0, and consider a Taylor expansion of the score function, V(\theta), about \theta_0:

### Statistics

**statisticalstatistical analysisstatistician**

In statistics, the score (or informant) is the gradient of the log-likelihood function with respect to the parameter vector.

### Gradient

**gradientsgradient vectorvector gradient**

In statistics, the score (or informant) is the gradient of the log-likelihood function with respect to the parameter vector. The score is the gradient (the vector of partial derivatives) of, the natural logarithm of the likelihood function, with respect to an m -dimensional parameter vector \theta.

### Statistical parameter

**parametersparameterparametrization**

In statistics, the score (or informant) is the gradient of the log-likelihood function with respect to the parameter vector.

### Slope

**gradientslopesgradients**

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.

### Infinitesimal

**infinitesimalsinfinitely closeinfinitesimally**

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.

### Continuous function

**continuouscontinuitycontinuous map**

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.

### Parameter space

**weight space**

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.

### Zero of a function

**rootrootszeros**

### Maxima and minima

**maximumminimumlocal maximum**

### Realization (probability)

**realizationrealizationsobserved data**

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.

### Sampling error

**sampling variabilitysampling variationless reliable**

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.

### Test statistic

**Common test statisticst''-test of test statistics**

### Integral

**integrationintegral calculusdefinite integral**

Further, the ratio of two likelihood functions evaluated at two distinct parameter values can be understood as a definite integral of the score function.

### Partial derivative

**partial derivativespartial differentiationpartial differential**

The score is the gradient (the vector of partial derivatives) of, the natural logarithm of the likelihood function, with respect to an m -dimensional parameter vector \theta.

### Natural logarithm

**lnnatural logarithmsnatural log**

The score is the gradient (the vector of partial derivatives) of, the natural logarithm of the likelihood function, with respect to an m -dimensional parameter vector \theta.

### Expected value

**expectationexpectedmean**

While the score is a function of \theta, it also depends on the observations at which the likelihood function is evaluated, and in view of the random character of sampling one may take its expected value over the sample space.

### Sample space

**event spacespacerepresented by points**

While the score is a function of \theta, it also depends on the observations at which the likelihood function is evaluated, and in view of the random character of sampling one may take its expected value over the sample space. To see this rewrite the likelihood function \mathcal L as a probability density function, and denote the sample space \mathcal{X}.

### Probability density function

**probability densitydensity functiondensity**

To see this rewrite the likelihood function \mathcal L as a probability density function, and denote the sample space \mathcal{X}.

### Leibniz integral rule

**differentiation under the integral signLeibniz's rulebasic form**

The assumed regularity conditions allow the interchange of derivative and integral (see Leibniz integral rule), hence the above expression may be rewritten as