# Parameter estimation for basis function model in Elements of Statistical Learning (ESL)

In the book Elements of Statistical Learning, section 2.8.3 describes Basis Functions, citing an example of a radial basis function as $$f_{\theta}(x) = \sum_{m=1}^M \beta_M \sigma(\alpha_m'x + b_m)$$, with $$\sigma(x)$$ as the activation function. This makes sense to me, but I am confused as to how the model is actually being fit. The given form of $$f_{\theta}(x)$$ that can be used to generate a prediction from $$x$$, but how are the parameters estimated?

Or, is the parameter fitting a separate question entirely? My intuition is that the RSS, $$\sum_{i=1}^N (y_i - f(x_i))^2$$ can still be minimized for parameter fitting. Would that be correct?

Sorry for the naive question. I am just trying to understand whether the class of the restricted estimator is linked in any way with the objective function we are trying to minimize?