Publications (41)
Online Pandora's Box for Contextual LLM Cascading
Alexandre Belloni, Yan Chen, Yehua Wei
Motivated by Large Language Model (LLM) cascading, we propose an online contextual Pandora's Box model for adaptively querying and selecting LLM APIs. In each period, a decision-ma…
Approximate group context tree
Alexandre Belloni, Roberto I. Oliveira
We study a variable length Markov chain model associated with a group of stationary processes that share the same context tree but each process has potentially different conditiona…
Subvector Inference in Partially Identified Models with Many Moment Inequalities
Alexandre Belloni, Federico Bugni, Victor Chernozhukov
This paper considers inference for a function of a parameter vector in a partially identified model with many moment inequalities. This framework allows the number of moment condit…
High Dimensional Latent Panel Quantile Regression with an Application to Asset Pricing
Alexandre Belloni, Mingli Chen, Oscar Hernan Madrid Padilla +2
We propose a generalization of the linear panel quantile regression model to accommodate both \textit{sparse} and \textit{dense} parts: sparse means while the number of covariates…
Simultaneous Confidence Intervals for High-dimensional Linear Models with Many Endogenous Variables
Alexandre Belloni, Christian Hansen, Whitney Newey
High-dimensional linear models with endogenous variables play an increasingly important role in recent econometric literature. In this work we allow for models with many endogenous…
On multivariate quantiles under partial orders
Alexandre Belloni, Robert L. Winkler
This paper focuses on generalizing quantiles from the ordering point of view. We propose the concept of partial quantiles, which are based on a given partial order. We establish th…
Sparse Models and Methods for Optimal Instruments with an Application to Eminent Domain
Alexandre Belloni, Daniel Chen, Victor Chernozhukov +1
We develop results for the use of Lasso and Post-Lasso methods to form first-stage predictions and estimate optimal instruments in linear instrumental variables (IV) models with ma…
Post-Selection Inference for Generalized Linear Models with Many Controls
Alexandre Belloni, Victor Chernozhukov, Ying Wei
This paper considers generalized linear models in the presence of many controls. We lay out a general methodology to estimate an effect of interest based on the construction of an…
Neighborhood Adaptive Estimators for Causal Inference under Network Interference
Alexandre Belloni, Fei Fang, Alexander Volfovsky
Estimating causal effects has become an integral part of most applied fields. In this work we consider the violation of the classical no-interference assumption with units connecte…
Uniform Post Selection Inference for LAD Regression and Other Z-estimation problems
Alexandre Belloni, Victor Chernozhukov, Kengo Kato
We develop uniformly valid confidence regions for regression coefficients in a high-dimensional sparse median regression model with homoscedastic errors. Our methods are based on a…
Escaping the Local Minima via Simulated Annealing: Optimization of Approximately Convex Functions
Alexandre Belloni, Tengyuan Liang, Hariharan Narayanan +1
We consider the problem of optimizing an approximately convex function over a bounded convex set in using only function evaluations. The problem is reduced to sampli…
Inference in High Dimensional Panel Models with an Application to Gun Control
Alexandre Belloni, Victor Chernozhukov, Christian Hansen +1
We consider estimation and inference in panel data models with additive unobserved individual specific heterogeneity in a high dimensional setting. The setting allows the number of…
High Dimensional Sparse Econometric Models: An Introduction
Alexandre Belloni, Victor Chernozhukov
In this chapter we discuss conceptually high dimensional sparse econometric models as well as estimation of these models using L1-penalization and post-L1-penalization methods. Foc…
Conditional Quantile Processes based on Series or Many Regressors
Alexandre Belloni, Victor Chernozhukov, Denis Chetverikov +1
Quantile regression (QR) is a principal regression method for analyzing the impact of covariates on outcomes. The impact is described by the conditional quantile function and its f…
Supplementary Appendix for "Inference on Treatment Effects After Selection Amongst High-Dimensional Controls"
Alexandre Belloni, Victor Chernozhukov, Christian Hansen
In this supplementary appendix we provide additional results, omitted proofs and extensive simulations that complement the analysis of the main text (arXiv:1201.0224).
Pivotal estimation via square-root Lasso in nonparametric regression
Alexandre Belloni, Victor Chernozhukov, Lie Wang
We propose a self-tuning method that simultaneously resolves three important practical problems in high-dimensional regression analysis, namely it handles…
Square-Root Lasso: Pivotal Recovery of Sparse Signals via Conic Programming
Alexandre Belloni, Victor Chernozhukov, Lie Wang
We propose a pivotal method for estimating high-dimensional sparse linear regression models, where the overall number of regressors is large, possibly much larger than , but…
LASSO Methods for Gaussian Instrumental Variables Models
Alexandre Belloni, Victor Chernozhukov, Christian Hansen
In this note, we propose to use sparse methods (e.g. LASSO, Post-LASSO, sqrt-LASSO, and Post-sqrt-LASSO) to form first-stage predictions and estimate optimal instruments in linear…
On the Behrens--Fisher problem: A globally convergent algorithm and a finite-sample study of the Wald, LR and LM Tests
Alexandre Belloni, Gustavo Didier
In this paper we provide a provably convergent algorithm for the multivariate Gaussian Maximum Likelihood version of the Behrens--Fisher Problem. Our work builds upon a formulation…
Inference for High-Dimensional Sparse Econometric Models
Alexandre Belloni, Victor Chernozhukov, Christian Hansen
This article is about estimation and inference methods for high dimensional sparse (HDS) regression models in econometrics. High dimensional sparse models arise in situations where…
Inference on Treatment Effects After Selection Amongst High-Dimensional Controls
Alexandre Belloni, Victor Chernozhukov, Christian Hansen
We propose robust methods for inference on the effect of a treatment variable on a scalar outcome in the presence of very many controls. Our setting is a partially linear model wit…
Linear and Conic Programming Estimators in High-Dimensional Errors-in-variables Models
Alexandre Belloni, Mathieu Rosenbaum, Alexandre Tsybakov
We consider the linear regression model with observation error in the design. In this setting, we allow the number of covariates to be much larger than the sample size. Several new…
Anti-Concentration Inequalities for the Difference of Maxima of Gaussian Random Vectors
Alexandre Belloni, Ethan X. Fang, Shuting Shen
We derive novel anti-concentration bounds for the difference between the maximal values of two Gaussian random vectors across various settings. Our bounds are dimension-free, scali…
Pivotal Estimation via Self-Normalization for High-Dimensional Linear Models with Error in Variables
Alexandre Belloni, Abhishek Kaul, Mathieu Rosenbaum
We propose a new estimator for the high-dimensional linear regression model with observation error in the design where the number of coefficients is potentially larger than the sam…
Confidence Bands for Coefficients in High Dimensional Linear Models with Error-in-variables
Alexandre Belloni, Victor Chernozhukov, Abhishek Kaul
We study high-dimensional linear models with error-in-variables. Such models are motivated by various applications in econometrics, finance and genetics. These models are challengi…
An -Regularization Approach to High-Dimensional Errors-in-variables Models
Alexandre Belloni, Mathieu Rosenbaum, Alexandre B. Tsybakov
Several new estimation methods have been recently proposed for the linear regression model with observation error in the design. Different assumptions on the data generating proces…
Program Evaluation and Causal Inference with High-Dimensional Data
Alexandre Belloni, Victor Chernozhukov, Ivan Fernández-Val +1
In this paper, we provide efficient estimators and honest confidence bands for a variety of treatment effects including local average (LATE) and local quantile treatment effects (L…
A high dimensional Central Limit Theorem for martingales, with applications to context tree models
Alexandre Belloni, Roberto I. Oliveira
We establish a central limit theorem for (a sequence of) multivariate martingales which dimension potentially grows with the length of the martingale. A consequence of the resu…
Some New Asymptotic Theory for Least Squares Series: Pointwise and Uniform Results
Alexandre Belloni, Victor Chernozhukov, Denis Chetverikov +1
In applications it is common that the exact form of a conditional expectation is unknown and having flexible functional forms can lead to improvements. Series method offers that by…
On the Computational Complexity of MCMC-based Estimators in Large Samples
Alexandre Belloni, Victor Chernozhukov
In this paper we examine the implications of the statistical large sample theory for the computational complexity of Bayesian and quasi-Bayesian estimation carried out using Metrop…
Adversarial Estimation of Assortment Probabilities under Independence Structure
Alexandre Belloni, Yan Chen, Matthew Harding
We consider the problem of estimating assortment probabilities, which is common in operations management applications, including product bundling, advertising, etc. Existing approa…
High-Dimensional Econometrics and Regularized GMM
Alexandre Belloni, Victor Chernozhukov, Denis Chetverikov +2
This chapter presents key concepts and theoretical results for analyzing estimation and inference in high-dimensional models. High-dimensional models are characterized by having a…
Posterior Inference in Curved Exponential Families under Increasing Dimensions
Alexandre Belloni, Victor Chernozhukov
This work studies the large sample properties of the posterior-based inference in the curved exponential family under increasing dimension. The curved structure arises from the imp…
Latent Agents in Networks: Estimation and Targeting
Baris Ata, Alexandre Belloni, Ozan Candogan
We consider a network of agents. Associated with each agent are her covariate and outcome. Agents influence each other's outcomes according to a certain connection/influence struct…
Ballot Design and Electoral Outcomes: The Role of Candidate Order and Party Affiliation
Alessandro Arlotto, Alexandre Belloni, Fei Fang +1
We develop a causal inference model to study how designing ballots with and without party designations impacts electoral outcomes when partisan voters rely on party-order cues to i…
L1-Penalized Quantile Regression in High-Dimensional Sparse Models
Alexandre Belloni, Victor Chernozhukov
We consider median regression and, more generally, a possibly infinite collection of quantile regressions in high-dimensional sparse models. In these models the overall number of r…
Uniformly Valid Post-Regularization Confidence Regions for Many Functional Parameters in Z-Estimation Framework
Alexandre Belloni, Victor Chernozhukov, Denis Chetverikov +1
In this paper we develop procedures to construct simultaneous confidence bands for potentially infinite-dimensional parameters after model selection for general moment c…
Valid Post-Selection Inference in High-Dimensional Approximately Sparse Quantile Regression Models
Alexandre Belloni, Victor Chernozhukov, Kengo Kato
This work proposes new inference methods for a regression coefficient of interest in a (heterogeneous) quantile regression model. We consider a high-dimensional model where the num…
Quantile Graphical Models: Prediction and Conditional Independence with Applications to Systemic Risk
Alexandre Belloni, Mingli Chen, Victor Chernozhukov
We propose two types of Quantile Graphical Models (QGMs) --- Conditional Independence Quantile Graphical Models (CIQGMs) and Prediction Quantile Graphical Models (PQGMs). CIQGMs ch…
quantreg.nonpar: An R Package for Performing Nonparametric Series Quantile Regression
Michael Lipsitz, Alexandre Belloni, Victor Chernozhukov +1
The R package quantreg.nonpar implements nonparametric quantile regression methods to estimate and make inference on partially linear quantile models. quantreg.nonpar obtains point…
Least squares after model selection in high-dimensional sparse models
Alexandre Belloni, Victor Chernozhukov
In this article we study post-model selection estimators that apply ordinary least squares (OLS) to the model selected by first-step penalized estimators, typically Lasso. It is we…