Model assembly (fitting)

• We want to define the distribution of a dependent variable $Y$ given $\underline{x}$.

• We usually do not evaluate the entire distribution, but just some of its characteristics, like:

  • Expected value (mean)
  • Variance
  • A Quantile

• A good model that can approximate conditional expected value $E_{Y|\underline{x}}(Y) \approx f(x)$ needs to reflect a satisfactory predictive performance.

• The Model fitting is a procedure of selecting a value for model coefficients $\underline{\theta} \in \Theta$ that minimizes some loss function $L()$:

$$\hat{\underline{\theta}} = \text{arg} \min_{\underline{\theta} \in \Theta} L \{ \underline{y}, f(\theta, X) \}$$