Parameter Estimation

Parameter estimationIt means using sample indicators to estimate overall indicators. Specifically, it is to use the sample mean to estimate the overall mean or to use the sample rate to estimate the overall rate.

The specific idea is to use fewer parameters to describe the overall distribution.

Commonly used parameter estimates

　 　
Commonly used parameter estimation methods include maximum likelihood estimation, Bayesian estimation and maximum a posteriori estimation.

• Maximum likelihood estimation treats the parameter to be estimated as a deterministic quantity whose value is unknown. Therefore, it is only necessary to obtain the best estimate, which is the value that maximizes the probability of generating the observed sample.

• Bayesian estimation treats the parameter to be estimated as a random variable that conforms to a certain prior probability distribution. Comparing the two methods, maximum likelihood estimation is simpler and has better convergence effect when the sample size increases.

• The maximum a posteriori probability estimation is to find the parameters when the likelihood function is maximized. The parameters obtained not only make the likelihood function large, but also the prior probability of its occurrence must be large.

Parameter estimation classification

There are usually two types of parameter estimation: point estimation and interval estimation.

• Point estimation means using a sample function to estimate the overall function.

• Interval estimation means using interval functions to estimate the overall function.

other

In addition to parameter estimation, there is another type of non-parametric estimation: when the category to which the sample belongs is known, but the form of the overall probability density function is unknown, it is required to directly infer the probability density function itself.