# Model Estimation

## 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.