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Estimation theory is a branch of statistics that deals with estimating the values of parameters based on measured empirical data that has a random component. The parameters describe an underlying physical setting in such a way that their value affects the distribution of the measured data.
In statistics, the method of estimating equations is a way of specifying how the parameters of a statistical model should be estimated. This can be thought of as a generalisation of many classical methods—the method of moments , least squares , and maximum likelihood —as well as some recent methods like M-estimators .
In statistics, the method of moments is a method of estimation of population parameters.The same principle is used to derive higher moments like skewness and kurtosis. It starts by expressing the population moments (i.e., the expected values of powers of the random variable under consideration) as functions of the parameters of interest.
An empirical likelihood ratio function is defined and used to obtain confidence intervals parameter of interest θ similar to parametric likelihood ratio confidence intervals. [7] [8] Let L(F) be the empirical likelihood of function , then the ELR would be: = / (). Consider sets of the form
To derive estimators for the parameters of probability distributions, applying the method of moments to the L-moments rather than conventional moments. In addition to doing these with standard moments, the latter (estimation) is more commonly done using maximum likelihood methods; however using L-moments provides a number of advantages.
An example is shown on the left. The parameter space has just two elements and each point on the graph corresponds to the risk of a decision rule: the x-coordinate is the risk when the parameter is and the y-coordinate is the risk when the parameter is . In this decision problem, the minimax estimator lies on a line segment connecting two ...
In statistics, maximum spacing estimation (MSE or MSP), or maximum product of spacing estimation (MPS), is a method for estimating the parameters of a univariate statistical model. [1] The method requires maximization of the geometric mean of spacings in the data, which are the differences between the values of the cumulative distribution ...
Estimation statistics, or simply estimation, is a data analysis framework that uses a combination of effect sizes, confidence intervals, precision planning, and meta-analysis to plan experiments, analyze data and interpret results. [1]