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Quadratic regression (QR) models naturally extend linear models by considering interaction effects between the covariates. To conduct model selection in QR, it is important to maintain the hierarchical model structure between main effects…
We develop a novel approach to tackle the common but challenging problem of conformal inference for missing data in machine learning, focusing on Missing at Random (MAR) data. We propose a new procedure Conformal prediction for Missing data…
This study aims to improve the spatial representation of uncertainties when regressing surface wind speeds from large-scale atmospheric predictors for sub-seasonal forecasting. Sub-seasonal forecasting often relies on large-scale…
Expectile regression is a nice tool for investigating conditional distributions beyond the conditional mean. It is well-known that expectiles can be described with the help of the asymmetric least square loss function, and this link makes…
Quantile regression is a powerful data analysis tool that accommodates heterogeneous covariate-response relationships. We find that by coupling the asymmetric Laplace working likelihood with appropriate shrinkage priors, we can deliver…
We propose a novel targeted maximum likelihood estimator (TMLE) for quantiles in semiparametric missing data models. Our proposed estimator is locally efficient, $\sqrt{n}$-consistent, asymptotically normal, and doubly robust, under…
Functional quantile regression (FQR) is a useful alternative to mean regression for functional data as it provides a comprehensive understanding of how scalar predictors influence the conditional distribution of functional responses. In…
This paper considers an extension of the multivariate symmetric Laplace distribution to matrix variate case. The symmetric Laplace distribution is a scale mixture of normal distribution. The maximum likelihood estimators (MLE) of the…
Timely characterizations of risks in economic and financial systems play an essential role in both economic policy and private sector decisions. However, the informational content of low-frequency variables and the results from conditional…
Quantile estimation is a problem presented in fields such as quality control, hydrology, and economics. There are different techniques to estimate such quantiles. Nevertheless, these techniques use an overall fit of the sample when the…
The Multi-Kink Quantile Regression (MKQR) model is an important tool for analyzing data with heterogeneous conditional distributions, especially when quantiles of response variable are of interest, due to its robustness to outliers and…
Penalized quantile regression (QR) is widely used for studying the relationship between a response variable and a set of predictors under data heterogeneity in high-dimensional settings. Compared to penalized least squares, scalable…
The conditional mean risk-sharing (CMRS) rule is an important tool for distributing aggregate losses across individual risks, but its implementation in continuous multivariate models typically requires complicated multidimensional…
The generalized Laplace (GL) distribution, which falls in the larger family of generalized hyperbolic distributions, provides a versatile model to deal with a variety of applications thanks to its shape parameters. The elliptically…
Quantile regression is a technique to estimate conditional quantile curves. It provides a comprehensive picture of a response contingent on explanatory variables. In a flexible modeling framework, a specific form of the conditional quantile…
Distributional reinforcement learning (DRL) enhances the understanding of the effects of the randomness in the environment by letting agents learn the distribution of a random return, rather than its expected value as in standard RL. At the…
In this work, we explore the theoretical properties of conditional deep generative models under the statistical framework of distribution regression where the response variable lies in a high-dimensional ambient space but concentrates…
Due to the dynamic nature of financial markets, maintaining models that produce precise predictions over time is difficult. Often the goal isn't just point prediction but determining uncertainty. Quantifying uncertainty, especially the…
Latent variable models represent a useful tool for the analysis of complex data when the constructs of interest are not observable. A problem related to these models is that the integrals involved in the likelihood function cannot be solved…
A mixture of shifted asymmetric Laplace distributions is introduced and used for clustering and classification. A variant of the EM algorithm is developed for parameter estimation by exploiting the relationship with the general inverse…