In pknight24/KPR: Kernel-penalized regression

Poster Formulas

Multiple regression $$\Huge\mathbf{Y} = \mathbf{X}\beta + \varepsilon$$

Ordinany least squares $$\Huge\hat{\beta}{OLS} =\mathop{\mathrm{arg\,min}}{\beta} \left{\Vert \mathbf{Y} - \mathbf{X}\beta \Vert^2_{2}\right}$$

Ridge $$\Huge\hat{\beta}{Ridge} =\mathop{\mathrm{arg\,min}}{\beta} \left{\Vert \mathbf{Y} - \mathbf{X}\beta \Vert^2_{2} + \lambda\Vert \beta \Vert^2_2\right}$$

KPR model $$\Huge\mathbf{Y} = \mathbf{Z}\beta + \mathbf{E}\eta + \varepsilon$$ KPR fit

$$\Huge\hat{\beta}, \hat{\eta} = \mathop{\mathrm{arg\,min}}{\beta, \eta} \left{\Vert \mathbf{Y} - \mathbf{Z}\beta - \mathbf{E}\eta \Vert^2{H} + \lambda\Vert \beta \Vert^2_{Q^{-1}}\right}$$

pknight24/KPR documentation built on Aug. 5, 2023, 7:01 a.m.