Stochastic kernel
Encyclopedia
In statistics
, a stochastic kernel estimate is an estimate of the transition function
of a (usually discrete-time) stochastic process
. Often, this is an estimate of the conditional density function obtained using kernel density estimation
. The estimated conditional distribution can then be used to derive estimates of other properties of the stochastic process
, such as the stationary distribution
.
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....
, a stochastic kernel estimate is an estimate of the transition function
Transition function
In mathematics, a transition function has several different meanings:* In topology, a transition function is a homeomorphism from one coordinate chart to another...
of a (usually discrete-time) stochastic process
Stochastic process
In probability theory, a stochastic process , or sometimes random process, is the counterpart to a deterministic process...
. Often, this is an estimate of the conditional density function obtained using kernel density estimation
Kernel (statistics)
A kernel is a weighting function used in non-parametric estimation techniques. Kernels are used in kernel density estimation to estimate random variables' density functions, or in kernel regression to estimate the conditional expectation of a random variable. Kernels are also used in time-series,...
. The estimated conditional distribution can then be used to derive estimates of other properties of the stochastic process
Stochastic process
In probability theory, a stochastic process , or sometimes random process, is the counterpart to a deterministic process...
, such as the stationary distribution
Stationary distribution
Stationary distribution may refer to:* The limiting distribution in a Markov chain* The marginal distribution of a stationary process or stationary time series* The set of joint probability distributions of a stationary process or stationary time series...
.
External links
- Conditional Stochastic Kernel Estimation by Nonparametric Methods (Laurini, Márcio P. & Valls Pereira, Pedro L.)