  Statistical inference under market equilibrium effects has attracted
increasing attention recently. In this paper we focus on the specific case of
linear Fisher markets. They have been widely use in fair resource allocation of
food/blood donations and budget management in large-scale Internet ad auctions.
In resource allocation, it is crucial to quantify the variability of the
resource received by the agents (such as blood banks and food banks) in
addition to fairness and efficiency properties of the systems. For ad auction
markets, it is important to establish statistical properties of the platform's
revenues in addition to their expected values. To this end, we propose a
statistical framework based on the concept of infinite-dimensional Fisher
markets. In our framework, we observe a market formed by a finite number of
items sampled from an underlying distribution (the "observed market") and aim
to infer several important equilibrium quantities of the underlying long-run
market. These equilibrium quantities include individual utilities, social
welfare, and pacing multipliers. Through the lens of sample average
approximation (SSA), we derive a collection of statistical results and show
that the observed market provides useful statistical information of the
long-run market. In other words, the equilibrium quantities of the observed
market converge to the true ones of the long-run market with strong statistical
guarantees. These include consistency, finite sample bounds, asymptotics, and
confidence. As an extension, we discuss revenue inference in quasilinear Fisher
markets.
