Projection matrix: Difference between revisions

Revision as of 19:44, 1 October 2020

Revision as of 19:46, 1 October 2020

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Suppose that we wish to estimate a linear model using linear least squares. The model can be written as

:<math>\mathbf{y} = \mathbf{X} \boldsymbol \beta + \boldsymbol \varepsilon,</math>

where ''<math>\mathbf{X''}</math> is a matrix of [[explanatory variable]]s (the [[design matrix]]), '''''β''''' is a vector of unknown parameters to be estimated, and '''''ε''''' is the error vector.

Many types of models and techniques are subject to this formulation. A few examples are [[linear least squares (mathematics)|linear least squares]], [[smoothing splines]], [[regression splines]], [[local regression]], [[kernel regression]], and [[linear filter]]ing.