ABSTRACT
Appendix A: R Code . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237 Appendix B: Description of the Variables of the Example in Section 13.2 . . . . . . . . . 238 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239
Suppose we observe an independent and identically distributed sample Z1, . . . , Zn of random variables with distribution P0, and assume that P0 is an element of a statistical model M. Suppose also that nothing is known about P0, so that M represents the nonparametric model. Statistical and machine learning are concerned with drawing inferences about target parameters η0 of the distribution P0. The types of parameters discussed in this chapter are typically functions η0 of z, which can be represented as the minimizer of the expectation of a loss function. Specifically, we consider parameters that may be defined as
η0 = argmin η∈F
∫ L(z, η) dP0(z), (13.1)
where F is a space of functions of z and L is a loss function of interest. The choice of space F and loss function L explicitly defines the estimation problem. Below we discuss some examples of parameters that may be defined as in Equation 13.1.
