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Using and extending fractional order statistic theory, we characterize the $O(n^{-1})$ coverage probability error of the previously proposed confidence intervals for population quantiles using $L$-statistics as endpoints in Hutson (1999).…
Quantile regression, based on check loss, is a widely used inferential paradigm in Econometrics and Statistics. The conditional quantiles provide a robust alternative to classical conditional means, and also allow uncertainty quantification…
We consider a linear regression model, with the parameter of interest a specified linear combination of the regression parameter vector. We suppose that, as a first step, a data-based model selection (e.g. by preliminary hypothesis tests or…
Quantile Regression (QR) provides a way to approximate a single conditional quantile. To have a more informative description of the conditional distribution, QR can be merged with deep learning techniques to simultaneously estimate multiple…
This paper develops a new framework, called modular regression, to utilize auxiliary information -- such as variables other than the original features or additional data sets -- in the training process of linear models. At a high level, our…
Quantile regression is a powerful tool for inferring how covariates affect specific percentiles of the response distribution. Existing methods either estimate conditional quantiles separately for each quantile of interest or estimate the…
Conformal prediction provides a principled framework for constructing predictive sets with finite-sample validity. While much of the focus has been on univariate response variables, existing multivariate methods either impose rigid…
Predictive inference under a general regression setting is gaining more interest in the big-data era. In terms of going beyond point prediction to develop prediction intervals, two main threads of development are conformal prediction and…
Quantile regression has demonstrated promising utility in longitudinal data analysis. Existing work is primarily focused on modeling cross-sectional outcomes, while outcome trajectories often carry more substantive information in practice.…
We develop a new approach to multi-label conformal prediction in which we aim to output a precise set of promising prediction candidates with a bounded number of incorrect answers. Standard conformal prediction provides the ability to adapt…
In practical applications, one often does not know the "true" structure of the underlying conditional quantile function, especially in the ultra-high dimensional setting. To deal with ultra-high dimensionality, quantile-adaptive marginal…
Uncertainty quantification in time series prediction is challenging due to the temporal dependence and distribution shift on sequential data. Conformal inference provides a pivotal and flexible instrument for assessing the uncertainty of…
Conformal prediction is widely used to equip black-box machine learning models with uncertainty quantification, offering formal coverage guarantees under exchangeable data. However, these guarantees fail when faced with subpopulation…
This paper develops a semi-parametric procedure for estimation of unconditional quantile partial effects using quantile regression coefficients. The estimator is based on an identification result showing that, for continuous covariates,…
Conformal prediction is an assumption-lean approach to generating distribution-free prediction intervals or sets, for nearly arbitrary predictive models, with guaranteed finite-sample coverage. Conformal methods are an active research topic…
This paper considers the problem of kernel regression and classification with possibly unobservable response variables in the data, where the mechanism that causes the absence of information is unknown and can depend on both predictors and…
We develop Temporal Quantile Adjustment (TQA), a general method to construct efficient and valid prediction intervals (PIs) for regression on cross-sectional time series data. Such data is common in many domains, including econometrics and…
We give a simple, generic conformal prediction method for sequential prediction that achieves target empirical coverage guarantees against adversarially chosen data. It is computationally lightweight -- comparable to split conformal…
Quantile regression is a powerful tool for learning the relationship between a response variable and a multivariate predictor while exploring heterogeneous effects. In this paper, we consider statistical inference for quantile regression…
This paper presents a new conformal method for generating simultaneous forecasting bands guaranteed to cover the entire path of a new random trajectory with sufficiently high probability. Prompted by the need for dependable uncertainty…