quantile regression

In multiple quantile regression, conventional multiple testing procedures fail to control the family-wise error rate (FWER) rigorously. To address this, we propose a multivariate joint test based on rank scores, embedded within a closed testing procedure to guarantee strong FWER control. This work constitutes the first extension of rank-score-based inference to simultaneous quantile regression, overcoming the low statistical power inherent in Bonferroni-type corrections. We establish the asymptotic validity of the proposed test under mild regularity conditions. Extensive Monte Carlo simulations demonstrate that the method maintains the nominal FWER level precisely across diverse simulation designs while delivering substantially higher statistical power than existing approaches.

This study addresses the failure of conventional instrumental variable (IV) methods when a policy alters the distribution of an endogenous variable without substantially affecting its mean. To tackle this challenge, the authors propose a distributional IV framework that formally introduces the concept of “distributional relevance” and demonstrates that purely distribution-shifting instruments can identify average structural effects. By integrating control function approaches with quantile regression, they develop a Quantile Least Squares (Q-LS) estimator that aggregates conditional quantiles into an optimal mean-square predictor, replacing traditional two-stage least squares (2SLS) and mitigating weak-instrument bias. Monte Carlo simulations confirm the estimator’s accuracy and reliable confidence interval coverage. An empirical application leverages distributional shifts in out-of-pocket risk induced by the Medicare Part D policy to more precisely estimate its effect on depression.

This study addresses the estimation and inference of τ-quantiles of heterogeneous slope coefficients in panel data, moving beyond the conventional focus on outcome heterogeneity. It proposes a two-step quantile regression framework to characterize the quantile features of the cross-sectional distribution of slope coefficients and establishes asymptotic theory under both random and fixed designs. The method relaxes conventional sample growth conditions, making it suitable for large-N settings and accommodating both √N and √(N√T) convergence rates. Two bootstrap procedures are developed to facilitate valid inference. Monte Carlo simulations and an empirical application to mutual fund data demonstrate the method’s effectiveness and reveal substantial heterogeneity in slope coefficients across different quantiles.

This study addresses the bias in quantile regression estimation arising from the coexistence of endogeneity and additive measurement error in the dependent variable. It is the first to achieve nonparametric identification of conditional quantile coefficient functions and other distributional parameters within a triangular system by integrating the control function approach with Copula modeling. To this end, the paper proposes a two-step sieve maximum likelihood estimator: first, the control function is estimated nonparametrically; then, it is treated as a generated regressor and incorporated into the sieve likelihood via Copula-based weights for maximization, with inference conducted using the bootstrap. Monte Carlo simulations demonstrate that the proposed method substantially reduces estimation bias and exhibits superior performance in scenarios where existing approaches fail.

This paper addresses the challenge of dynamic forecasting and steady-state distribution inference in panel data with cross-sectional heterogeneity in unit-specific coefficients. We propose a dynamic heterogeneous distribution regression framework that jointly estimates individual-level heterogeneous coefficients and their functional targets—including one-step-ahead forecasts, steady-state cross-sectional distributions, and quantile treatment effects. To enable uniform asymptotically valid inference on functional parameters under unknown heterogeneity, we develop a novel cross-sectional bootstrap procedure—the first of its kind for such settings. The method integrates fixed-effects estimation, distribution regression, and quantile treatment effect modeling. Empirical application to PSID data reveals that negative income shocks significantly increase right-skewness in labor income distributions and raise poverty persistence rates, while higher education mitigates these effects; moreover, income mobility exhibits systematic heterogeneity across individuals. Simulation studies confirm the method’s robustness and reliability.

Existing quantile estimation methods struggle to ensure consistency when censoring, endogenous regressors, and conditional heteroskedasticity coexist, thereby limiting accurate identification of heterogeneous economic effects. This study proposes a two-step sequential control function censored quantile (SCFCQ) estimator, which for the first time integrates the control function approach with sequential quantile regression to effectively address identification of distributional effects in the presence of unbounded endogeneity and heteroskedasticity. The method enjoys strong theoretical properties and computational tractability. Applied to the UK Family Expenditure Survey data, it successfully uncovers the heterogeneous distribution of income elasticities across household preference dimensions, demonstrating both robustness and empirical relevance.

This study addresses the computational and inferential challenges of applying predictive augmented inference to quantile regression in data-limited settings characterized by few high-quality labels and abundant proxy labels. The authors introduce convolution smoothing into this framework for the first time, proposing two computable estimators—along with an ensemble approach—by smoothing the check loss function. This strategy effectively mitigates optimization difficulties arising from the non-differentiability of the original objective and substantially reduces over-coverage in confidence intervals. Theoretical analysis establishes the asymptotic distribution under model misspecification, while numerical experiments and an application to housing data demonstrate that the proposed method is computationally efficient, yields accurate inference, and offers both practical utility and superior performance.

This study addresses the identification and estimation of common slope coefficients in quantile regression models with short panel data, accommodating unrestricted individual effects and temporally stationary disturbances. Under a stationarity assumption on the error term, the authors propose a two-step minimum distance estimator for fixed time dimension \(T\): first, a differencing identification strategy is constructed via intertemporal quantile regression projections, circumventing explicit estimation of individual effects; second, this restriction is leveraged to identify slope coefficients that are invariant across quantiles. The resulting estimator accommodates arbitrary within-individual serial correlation, achieves \(\sqrt{n}\)-consistency and asymptotic normality, and is accompanied by an analytical covariance estimator, a cluster-robust bootstrap procedure, and an overidentification test. Monte Carlo simulations demonstrate its excellent finite-sample performance across a range of data-generating processes.

This study addresses the challenge of obtaining consistent estimators in quantile regression when covariates are subject to normal measurement error, a setting complicated by the discontinuity and nonlinearity of the check loss function. The authors propose a novel estimation approach applicable to both linear and nonlinear models, which employs kernel smoothing to handle discontinuities and leverages complex-domain extensions together with moment-generating functions to manage nonlinearity—without requiring joint modeling across multiple quantiles. Within a general quantile regression framework, this work establishes, for the first time, an estimator that achieves root-n consistency and asymptotic normality. Theoretical analysis confirms the standard convergence rate, while numerical simulations and an empirical application to the 2024 Japanese cherry blossom bloom dates demonstrate the method’s practical effectiveness.

This study addresses the challenge of statistical inference for quantile regression in two-way clustered data with complex dependence structures. The authors propose a robust sandwich variance estimator grounded in the framework of exchangeable arrays and a decomposition of quantile score projections: the "bread" component is constructed via kernel density estimation, while the "meat" component is built through projection matching. Building on this estimator, they develop a self-normalized Gaussian approximation theory, establishing its consistency and valid inferential properties under Gaussian interaction regimes. They further demonstrate the impossibility of consistent inference in non-Gaussian settings. Theoretical analysis reveals that the convergence rate is jointly determined by the two-way clustering structure.