Model Estimation
Contents
Definition
Model Estimation (also Model Fit) is a general term denoting the precise quantitative procedure by which a quantitative (risk) model is developed, specifically the methodology by which its Model Parameters are derived
A related term is Model Calibration (which may involve additional non-quantitative elements)
Estimation Methodologies
Estimation methodologies vary with the type of statistical model considered (number of parameters, nature of distributions etc)
Ordinary least squares
wikipedia:Ordinary least squares (OLS) is a type of linear least squares method for estimating the unknown parameters in a linear regression model
Maximum Likelihood
A common methodology is wikipedia:Maximum likelihood estimation (MLE), which involves calculating a likelihood function based on a possible set of model parameters and observed data. Once the resulting probability function is determined, the set of parameters that maximize the likelihood function can be determined.
Generalized method of moments
The wikipedia:Generalized method of moments is a generic method for estimating parameters in statistical models. Usually it is applied in the context of semiparametric models, where the parameter of interest is finite-dimensional, whereas the full shape of the data's distribution function may not be known, and therefore maximum likelihood estimation is not applicable
Kalman Filtering
The second methodology is the wikipedia:Kalman filter (linear quadratic estimation (LQE)), which involves consecutive cycles of predicting the state of an observed variable based on a model, comparing that prediction with the realized outcome in the historical observed data, and updating the parameters to achieve optimal predictive power.
