Bandit algorithms generate data for downstream inference, but adaptive sampling biases post-bandit sample means. We analyze this bias for stable index algorithms, including UCB1 and its generalizations, and derive sharp leading-order expressions for the sample-mean bias and expected $Z$-statistic. Our characterization reveals the algorithmic origin of bias through a key index-function-dependent quantity, which we term effective exploration rate. For example, under UCB1, the effective exploration rate is of order $\sqrt{\log T}$, and the standardized bias of any arm (that is not uniquely optimal) decays at the extremely slow rate $1/\sqrt{\log T}$. We also show how the choice of the index function affects both regret and bias, which reveals a regret-bias trade-off: more exploratory algorithm reduces bias but increases regret. Our sharp characterization for bias uses a novel empirical fluid approximation of the algorithm's sampling dynamics, which may be of independent interest.
A one-step estimator with K-fold cross-fitting and a U-statistic correction of the squared loss that removes the Monte Carlo bias of the naive plug-in is proposed, which is $\sqrt{n}$-consistent and asymptotically normal under double-robust rate conditions, and the resulting Wald interval attains nominal coverage.
To design systems that are protected against events much rarer than the observational record, extreme-value methods are needed to extrapolate distribution tails. Tail-index estimators such as the Hill estimator are central to this extrapolation, but overestimating the tail exponent can lead to substantial underestimati...
Martijn Gösgens, B. V. Van Parys, Bert Zwart· 0 citations
A simple decomposition of a neural-network-based normalizing flow that naturally uncovers a pivotal statistic in the presence of nuisance parameters, based only on a sample generator from the distribution of interest is presented.
This paper develops Wald inference for least-squares estimation of linear regression models on dyadic data, accommodating configurations where multiple observations share the same pair of units (e.g., directed flows, multilayer networks, and dyadic panels). We establish that the dyadic-robust Wald statistic is asymptot...
Benjamin O. Harrison, David T. Jacho-Chávez· 0 citations
Econometric models offer parsimonious but inexact approximations to data-generating processes. This paper studies the generalized method of moments (GMM) when exchangeable specification errors of order $n^{-1/2}$ contaminate the moment conditions. I develop estimators for the mean and variance of these specification er...
Researchers typically collect experimental data sequentially, allowing early outcome observations and adaptive treatment assignment to reduce exposure to inferior treatments. In this article, we review multiarmed bandit adaptive experimental designs that balance exploration and exploitation. Because adaptively collecte...
Jan Kemper, Davud Rostam-Afschar· The Stata Journal· 1 citation
