ABSTRACT
Consider the problem of building regression models that examine the relationship between a dependent variable y and multiple independent variables x1, . . . , xd. For generality, let the domain of each xk be an arbitrary set Xk. Denote x = (x1, . . . , xd). Given observations (xi, yi) for i = 1, . . . , n, where xi = (xi1, . . . , xid), a multiple regression model relates the dependent variable and independent variables as follows:
yi = f(xi) + ǫi, i = 1, . . . , n, (4.1)
where f is a multivariate regression function, and ǫi are zero-mean independent random errors with a common variance σ2. The goal is to construct a model for f and estimate it based on noisy data.
