Mean integrated squared error
Encyclopedia
In statistics
, the mean integrated squared error (MISE) is used in density estimation
. The MISE of an estimate
of an unknown probability density
is given by
where ƒ is the unknown density, ƒn is its estimate based on a sample
of n iid random variables.
Here, E denotes the expected value
with respect to that sample.
The MISE is also known as L2 risk function
.
Statistics
Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....
, the mean integrated squared error (MISE) is used in density estimation
Density estimation
In probability and statistics,density estimation is the construction of an estimate, based on observed data, of an unobservable underlying probability density function...
. The MISE of an estimate
Estimator
In statistics, an estimator is a rule for calculating an estimate of a given quantity based on observed data: thus the rule and its result are distinguished....
of an unknown probability density
Probability density
Probability density may refer to:* Probability density function in probability theory* The product of the probability amplitude with its complex conjugate in quantum mechanics...
is given by
where ƒ is the unknown density, ƒn is its estimate based on a sample
Sample (statistics)
In statistics, a sample is a subset of a population. Typically, the population is very large, making a census or a complete enumeration of all the values in the population impractical or impossible. The sample represents a subset of manageable size...
of n iid random variables.
Here, E denotes the expected value
Expected value
In probability theory, the expected value of a random variable is the weighted average of all possible values that this random variable can take on...
with respect to that sample.
The MISE is also known as L2 risk function
Risk function
In decision theory and estimation theory, the risk function R of a decision rule, δ, is the expected value of a loss function L:...
.
See also
- Minimum distance estimationMinimum distance estimationMinimum distance estimation is a statistical method for fitting a mathematical model to data, usually the empirical distribution.-Definition:...
- Mean squared errorMean squared errorIn statistics, the mean squared error of an estimator is one of many ways to quantify the difference between values implied by a kernel density estimator and the true values of the quantity being estimated. MSE is a risk function, corresponding to the expected value of the squared error loss or...