Robust Confidence Regions for Incomplete Models

Abstract

We provide details on how to implement the inference method proposed in the main text.

A Central Limit Theorem, Loss Aversion and Multi-Armed Bandits

“…This latter assumption of "symmetry" within each arm is known as partial exchangeability, a property introduced by de Finetti (1938), who also showed that it implies conditional independence as in (i), and, in fact, that it characterizes a representation such as in (4.18). 15 This example satisfies all the assumptions of the more general case above and thus all the preceding results apply. Moreover, the added structure assumed herein permits sharper results, specifically regarding supporting strategies and what is learned asymptotically.…”

“…n are just the 1-step-ahead conditionals of P s 15. The stronger property of exchangeability, which is better known, assumes interchangeability also across distinct arms and thus views the two arms as being identical, which is excluded in our case because of (4.14) and p = p. SeeLink (1980) andDiaconis and Freedman (1982) for more on partial exchangeability andKallenberg (2005) for a comprehensive treatment of probabilistic symmetries.…”

Central limit theorems for bounded random variables under belief measures

“…But he only considers CLTs for unidirectional intervals which looks the same as the classical CLTs as long as the partial sums of {X i } ∞ i=1 is standardized by proper parameters. As we have mentioned, Theorem 3.1 in Epstein et al [9] is the first result concerning CLTs for two-sided intervals under belief measures. And it has a nice application in Jovanovic entry game and binary experiments, or more generally, in an environment where the agent does not have enough information to formulate a probability prediction so he can only hold a coarse picture (belief) about the uncertainty.…”

“…But Theorem 3.1 in [9] considers only Bernoulli random variables which limit the potential application of the CLTs for belief measures. If one were in a belief measure world with general (continuum) state space and general bounded random variables, Theorem 1.1 does not work.…”

Inference in Models of Discrete Choice with Social Interactions Using Network Data

“…Then the same underlying random vector determines equilibrium selection in both components, so their outcomes are correlated. In the cross-sectional setting, this problem is analogous to having a selection mechanism simultaneously determine equilibrium realizations across a set of distinct games, a scenario implicitly ruled out when researchers assume separate realizations of the same game are independent (Epstein et al, 2016).…”