English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this paper, we study nonparametric estimation of instrumental variable(IV) regressions. Recently, many flexible machine learning methods have beendeveloped for instrumental variable estimation. However, these methods have atleast one of the following limitations: (1) restricting the IV regression to beuniquely identified; (2) only obtaining estimation error rates in terms ofpseudometrics (\emph{e.g.,} projected norm) rather than valid metrics(\emph{e.g.,} $L_2$ norm); or (3) imposing the so-called closedness conditionthat requires a certain conditional expectation operator to be sufficientlysmooth. In this paper, we present the first method and analysis that can avoidall three limitations, while still permitting general function approximation.Specifically, we propose a new penalized minimax estimator that can converge toa fixed IV solution even when there are multiple solutions, and we derive astrong $L_2$ error rate for our estimator under lax conditions. Notably, thisguarantee only needs a widely-used source condition and realizabilityassumptions, but not the so-called closedness condition. We argue that thesource condition and the closedness condition are inherently conflicting, sorelaxing the latter significantly improves upon the existing literature thatrequires both conditions. Our estimator can achieve this improvement because itbuilds on a novel formulation of the IV estimation problem as a constrainedoptimization problem.

Minimax Instrumental Variable Regression and $L_2$ Convergence Guarantees without Identification or Closedness