arXiv subjects

Denis Chetverikov

Publications and source records attributed to Denis Chetverikov.

At least 19 recordsLinked to original sources

arXiv2026

Asymptotic Variance Theory for Trimmed Least Squares and Trimmed Least Absolute Deviations in Censored Panel Models with Fixed Effects

We study inference using trimmed least squares (TLS) and trimmed least absolute deviations (TLAD) estimators of \citet{honore_trimmed_1992} in censored two-period panel-data models with fixed effects. We show that the published asymptotic variance formulas rely on additional regularity conditions that are not fully stated in the original analysis. For TLS, the published Hessian formula requires that the regressor-difference index vanish only when the regressor difference itself is zero, a restriction not explicitly stated in the original paper and violated, for instance, with a zero parameter vector. We derive the correct Hessian, establish asymptotic normality without imposing this restriction, and obtain a consistent plug-in variance estimator. We also show that the Hessian estimator proposed in \citet{honore_trimmed_1992} {\em is} actually consistent for the {\em correct} TLS asymptotic variance. For TLAD, we show that the published variance formula omits a conditional-probability term and that asymptotic normality requires additional continuity conditions. Under these conditions, we derive the corrected asymptotic variance and provide a tuning-parameter-free bootstrap variance estimator.

econ.EM↗

arXiv2026

Triple/Double-Debiased Lasso

In this paper, we propose a triple (or double-debiased) Lasso estimator for inference on a low-dimensional parameter in high-dimensional linear regression models. The estimator is based on a moment function that satisfies not only first- but also second-order Neyman orthogonality conditions, thereby eliminating both the leading bias and the second-order bias induced by regularization. We derive an asymptotic linear representation for the proposed estimator and show that its remainder terms are never larger and are often smaller in order than those in the corresponding asymptotic linear representation for the standard double Lasso estimator. Because of this improvement, the triple Lasso estimator often yields more accurate finite-sample inference and confidence intervals with better coverage. Monte Carlo simulations confirm these gains. In addition, we provide a general recursive formula for constructing higher-order Neyman orthogonal moment functions in Z-estimation problems, which underlies the proposed estimator as a special case.

econ.EM↗

arXiv2025

Higher-Order Asset Pricing Factors via Forward Selection Fama-MacBeth Regression

We show that the higher-order terms and interactions of the common sparse linear factors are significantly priced in the cross-section of equity returns. A higher-order model with only a small number of selected higher-order terms from six widely used factors outperforms traditional benchmarks both in-sample and out-of-sample. It also substantially reduces the alphas of the extensive factor zoo, suggesting that the pricing power of many zoo factors is attributable to their exposure to higher-order terms of common linear factors. We identify and rank the most relevant higher-order terms by developing a forward selection Fama-MacBeth procedure.

econ.EM↗

arXiv2024

Tuning parameter selection in econometrics

I review some of the main methods for selecting tuning parameters in nonparametric and $\ell_1$-penalized estimation. For the nonparametric estimation, I consider the methods of Mallows, Stein, Lepski, cross-validation, penalization, and aggregation in the context of series estimation. For the $\ell_1$-penalized estimation, I consider the methods based on the theory of self-normalized moderate deviations, bootstrap, Stein's unbiased risk estimation, and cross-validation in the context of Lasso estimation. I explain the intuition behind each of the methods and discuss their comparative advantages. I also give some extensions.

econ.EM↗

arXiv2024

One Factor to Bind the Cross-Section of Returns

We propose a new non-linear single-factor asset pricing model $r_{it}=h(f_{t}λ_{i})+ε_{it}$. Despite its parsimony, this model represents exactly any non-linear model with an arbitrary number of factors and loadings -- a consequence of the Kolmogorov-Arnold representation theorem. It features only one pricing component $h(f_{t}λ_{I})$, comprising a nonparametric link function of the time-dependent factor and factor loading that we jointly estimate with sieve-based estimators. Using 171 assets across major classes, our model delivers superior cross-sectional performance with a low-dimensional approximation of the link function. Most known finance and macro factors become insignificant controlling for our single-factor.

q-fin.GN↗

arXiv2024

csranks: An R Package for Estimation and Inference Involving Ranks

This article introduces the R package csranks for estimation and inference involving ranks. First, we review methods for the construction of confidence sets for ranks, namely marginal and simultaneous confidence sets as well as confidence sets for the identities of the tau-best. Second, we review methods for estimation and inference in regressions involving ranks. Third, we describe the implementation of these methods in csranks and illustrate their usefulness in two examples: one about the quantification of uncertainty in the PISA ranking of countries and one about the measurement of intergenerational mobility using rank-rank regressions.

econ.EM↗

arXiv2023

Logit-based alternatives to two-stage least squares

We propose logit-based IV and augmented logit-based IV estimators that serve as alternatives to the traditionally used 2SLS estimator in the model where both the endogenous treatment variable and the corresponding instrument are binary. Our novel estimators are as easy to compute as the 2SLS estimator but have an advantage over the 2SLS estimator in terms of causal interpretability. In particular, in certain cases where the probability limits of both our estimators and the 2SLS estimator take the form of weighted-average treatment effects, our estimators are guaranteed to yield non-negative weights whereas the 2SLS estimator is not.

econ.EM↗

arXiv2023

Inference for Rank-Rank Regressions

The slope coefficient in a rank-rank regression is a popular measure of intergenerational mobility. In this article, we first show that commonly used inference methods for this slope parameter are invalid. Second, when the underlying distribution is not continuous, the OLS estimator and its distribution may be sensitive to how ties in the ranks are handled. Motivated by these findings we derive the asymptotic distribution of the OLS estimator and provide valid inference methods for a general class of rank-rank regression specifications.

econ.EM↗

arXiv2023

Standard errors when a regressor is randomly assigned

We examine asymptotic properties of the OLS estimator when the values of the regressor of interest are assigned randomly and independently of other regressors. We find that the OLS variance formula in this case is often simplified, sometimes substantially. In particular, when the regressor of interest is independent not only of other regressors but also of the error term, the textbook homoskedastic variance formula is valid even if the error term and auxiliary regressors exhibit a general dependence structure. In the context of randomized controlled trials, this conclusion holds in completely randomized experiments with constant treatment effects. When the error term is heteroscedastic with respect to the regressor of interest, the variance formula has to be adjusted not only for heteroscedasticity but also for correlation structure of the error term. However, even in the latter case, some simplifications are possible as only a part of the correlation structure of the error term should be taken into account. In the context of randomized control trials, this implies that the textbook homoscedastic variance formula is typically not valid if treatment effects are heterogenous but heteroscedasticity-robust variance formulas are valid if treatment effects are independent across units, even if the error term exhibits a general dependence structure. In addition, we extend the results to the case when the regressor of interest is assigned randomly at a group level, such as in randomized control trials with treatment assignment determined at a group (e.g., school/village) level.

econ.EM↗

arXiv2022

Spectral and post-spectral estimators for grouped panel data models

In this paper, we develop spectral and post-spectral estimators for grouped panel data models. Both estimators are consistent in the asymptotics where the number of observations $N$ and the number of time periods $T$ simultaneously grow large. In addition, the post-spectral estimator is $\sqrt{NT}$-consistent and asymptotically normal with mean zero under the assumption of well-separated groups even if $T$ is growing much slower than $N$. The post-spectral estimator has, therefore, theoretical properties that are comparable to those of the grouped fixed-effect estimator developed by Bonhomme and Manresa (2015). In contrast to the grouped fixed-effect estimator, however, our post-spectral estimator is computationally straightforward.

econ.EM↗

arXiv2022

Improved Central Limit Theorem and bootstrap approximations in high dimensions

This paper deals with the Gaussian and bootstrap approximations to the distribution of the max statistic in high dimensions. This statistic takes the form of the maximum over components of the sum of independent random vectors and its distribution plays a key role in many high-dimensional econometric problems. Using a novel iterative randomized Lindeberg method, the paper derives new bounds for the distributional approximation errors. These new bounds substantially improve upon existing ones and simultaneously allow for a larger class of bootstrap methods.

math.ST↗

arXiv2022

High-dimensional Data Bootstrap

This article reviews recent progress in high-dimensional bootstrap. We first review high-dimensional central limit theorems for distributions of sample mean vectors over the rectangles, bootstrap consistency results in high dimensions, and key techniques used to establish those results. We then review selected applications of high-dimensional bootstrap: construction of simultaneous confidence sets for high-dimensional vector parameters, multiple hypothesis testing via stepdown, post-selection inference, intersection bounds for partially identified parameters, and inference on best policies in policy evaluation. Finally, we also comment on a couple of future research directions.

math.ST↗

arXiv2022

Weighted-average quantile regression

In this paper, we introduce the weighted-average quantile regression framework, $\int_0^1 q_{Y|X}(u)ψ(u)du = X'β$, where $Y$ is a dependent variable, $X$ is a vector of covariates, $q_{Y|X}$ is the quantile function of the conditional distribution of $Y$ given $X$, $ψ$ is a weighting function, and $β$ is a vector of parameters. We argue that this framework is of interest in many applied settings and develop an estimator of the vector of parameters $β$. We show that our estimator is $\sqrt T$-consistent and asymptotically normal with mean zero and easily estimable covariance matrix, where $T$ is the size of available sample. We demonstrate the usefulness of our estimator by applying it in two empirical settings. In the first setting, we focus on financial data and study the factor structures of the expected shortfalls of the industry portfolios. In the second setting, we focus on wage data and study inequality and social welfare dependence on commonly used individual characteristics.

econ.EM↗

arXiv2021

Nearly optimal central limit theorem and bootstrap approximations in high dimensions

In this paper, we derive new, nearly optimal bounds for the Gaussian approximation to scaled averages of $n$ independent high-dimensional centered random vectors $X_1,\dots,X_n$ over the class of rectangles in the case when the covariance matrix of the scaled average is non-degenerate. In the case of bounded $X_i$'s, the implied bound for the Kolmogorov distance between the distribution of the scaled average and the Gaussian vector takes the form $$C (B^2_n \log^3 d/n)^{1/2} \log n,$$ where $d$ is the dimension of the vectors and $B_n$ is a uniform envelope constant on components of $X_i$'s. This bound is sharp in terms of $d$ and $B_n$, and is nearly (up to $\log n$) sharp in terms of the sample size $n$. In addition, we show that similar bounds hold for the multiplier and empirical bootstrap approximations. Moreover, we establish bounds that allow for unbounded $X_i$'s, formulated solely in terms of moments of $X_i$'s. Finally, we demonstrate that the bounds can be further improved in some special smooth and zero-skewness cases.

math.PR↗

arXiv2021

Selecting Penalty Parameters of High-Dimensional M-Estimators using Bootstrapping after Cross-Validation

We develop a new method for selecting the penalty parameter for $\ell_{1}$-penalized M-estimators in high dimensions, which we refer to as bootstrapping after cross-validation. We derive rates of convergence for the corresponding $\ell_1$-penalized M-estimator and also for the post-$\ell_1$-penalized M-estimator, which refits the non-zero entries of the former estimator without penalty in the criterion function. We demonstrate via simulations that our methods are not dominated by cross-validation in terms of estimation errors and can outperform cross-validation in terms of inference. As an empirical illustration, we revisit Fryer Jr (2019), who investigated racial differences in police use of force, and confirm his findings.

math.ST↗

arXiv2020

On cross-validated Lasso in high dimensions

In this paper, we derive non-asymptotic error bounds for the Lasso estimator when the penalty parameter for the estimator is chosen using $K$-fold cross-validation. Our bounds imply that the cross-validated Lasso estimator has nearly optimal rates of convergence in the prediction, $L^2$, and $L^1$ norms. For example, we show that in the model with the Gaussian noise and under fairly general assumptions on the candidate set of values of the penalty parameter, the estimation error of the cross-validated Lasso estimator converges to zero in the prediction norm with the $\sqrt{s\log p / n}\times \sqrt{\log(p n)}$ rate, where $n$ is the sample size of available data, $p$ is the number of covariates, and $s$ is the number of non-zero coefficients in the model. Thus, the cross-validated Lasso estimator achieves the fastest possible rate of convergence in the prediction norm up to a small logarithmic factor $\sqrt{\log(p n)}$, and similar conclusions apply for the convergence rate both in $L^2$ and in $L^1$ norms. Importantly, our results cover the case when $p$ is (potentially much) larger than $n$ and also allow for the case of non-Gaussian noise. Our paper therefore serves as a justification for the widely spread practice of using cross-validation as a method to choose the penalty parameter for the Lasso estimator.

math.ST↗

arXiv2019

Uniformly Valid Post-Regularization Confidence Regions for Many Functional Parameters in Z-Estimation Framework

In this paper we develop procedures to construct simultaneous confidence bands for $\tilde p$ potentially infinite-dimensional parameters after model selection for general moment condition models where $\tilde p$ is potentially much larger than the sample size of available data, $n$. This allows us to cover settings with functional response data where each of the $\tilde p$ parameters is a function. The procedure is based on the construction of score functions that satisfy certain orthogonality condition. The proposed simultaneous confidence bands rely on uniform central limit theorems for high-dimensional vectors (and not on Donsker arguments as we allow for $\tilde p \gg n$). To construct the bands, we employ a multiplier bootstrap procedure which is computationally efficient as it only involves resampling the estimated score functions (and does not require resolving the high-dimensional optimization problems). We formally apply the general theory to inference on regression coefficient process in the distribution regression model with a logistic link, where two implementations are analyzed in detail. Simulations and an application to real data are provided to help illustrate the applicability of the results.

stat.ME↗

arXiv2018

Inference on causal and structural parameters using many moment inequalities

This paper considers the problem of testing many moment inequalities where the number of moment inequalities, denoted by $p$, is possibly much larger than the sample size $n$. There is a variety of economic applications where solving this problem allows to carry out inference on causal and structural parameters, a notable example is the market structure model of Ciliberto and Tamer (2009) where $p=2^{m+1}$ with $m$ being the number of firms that could possibly enter the market. We consider the test statistic given by the maximum of $p$ Studentized (or $t$-type) inequality-specific statistics, and analyze various ways to compute critical values for the test statistic. Specifically, we consider critical values based upon (i) the union bound combined with a moderate deviation inequality for self-normalized sums, (ii) the multiplier and empirical bootstraps, and (iii) two-step and three-step variants of (i) and (ii) by incorporating the selection of uninformative inequalities that are far from being binding and a novel selection of weakly informative inequalities that are potentially binding but do not provide first order information. We prove validity of these methods, showing that under mild conditions, they lead to tests with the error in size decreasing polynomially in $n$ while allowing for $p$ being much larger than $n$, indeed $p$ can be of order $\exp (n^{c})$ for some $c > 0$. Importantly, all these results hold without any restriction on the correlation structure between $p$ Studentized statistics, and also hold uniformly with respect to suitably large classes of underlying distributions. Moreover, in the online supplement, we show validity of a test based on the block multiplier bootstrap in the case of dependent data under some general mixing conditions.

math.ST↗