  The Wald development of statistical decision theory addresses decision making
with sample data. Wald's concept of a statistical decision function (SDF)
embraces all mappings of the form [data -> decision]. An SDF need not perform
statistical inference; that is, it need not use data to draw conclusions about
the true state of nature. Inference-based SDFs have the sequential form [data
-> inference -> decision]. This paper motivates inference-based SDFs as
practical procedures for decision making that may accomplish some of what Wald
envisioned. The paper first addresses binary choice problems, where all SDFs
may be viewed as hypothesis tests. It next considers as-if optimization, which
uses a point estimate of the true state as if the estimate were accurate. It
then extends this idea to as-if maximin and minimax-regret decisions, which use
point estimates of some features of the true state as if they were accurate.
The paper primarily uses finite-sample maximum regret to evaluate the
performance of inference-based SDFs. To illustrate abstract ideas, it presents
specific findings concerning treatment choice and point prediction with sample
data.
