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Quantile regression \parencite{Koenker1978} is a robust and practically useful way to efficiently model quantile varying correlation and predict varied response quantiles of interest. This article constructs and tests MM algorithms, which…
Distributionally robust optimization (DRO) and invariant risk minimization (IRM) are two popular methods proposed to improve out-of-distribution (OOD) generalization performance of machine learning models. While effective for small models,…
Partial least squares (PLS) is a dimensionality reduction technique used as an alternative to ordinary least squares (OLS) in situations where the data is colinear or high dimensional. Both PLS and OLS provide mean based estimates, which…
We consider covariance estimation in the multivariate generalized Gaussian distribution (MGGD) and elliptically symmetric (ES) distribution. The maximum likelihood optimization associated with this problem is non-convex, yet it has been…
This paper presents a feasibility study demonstrating that quantum machine learning (QML) algorithms achieve competitive performance on real-world medical imaging despite operating under severe constraints. We evaluate Equilibrium…
A key challenge in probabilistic regression is ensuring that predictive distributions accurately reflect true empirical uncertainty. Minimizing overall prediction error often encourages models to prioritize informativeness over calibration,…
Several disciplines, like the social sciences, epidemiology, sentiment analysis, or market research, are interested in knowing the distribution of the classes in a population rather than the individual labels of the members thereof.…
Quantile regression is a powerful tool capable of offering a richer view of the data as compared to least-squares regression. Quantile regression is typically performed individually on a few quantiles or a grid of quantiles without…
We consider estimating a low-dimensional parameter in an estimating equation involving high-dimensional nuisances that depend on the parameter. A central example is the efficient estimating equation for the (local) quantile treatment effect…
Distributional reinforcement learning (RL) has proven useful in multiple benchmarks as it enables approximating the full distribution of returns and extracts rich feedback from environment samples. The commonly used quantile regression…
This paper investigates the quasi-maximum likelihood inference including estimation, model selection and diagnostic checking for linear double autoregressive (DAR) models, where all asymptotic properties are established under only…
This paper proposes a novel conditional heteroscedastic time series model by applying the framework of quantile regression processes to the ARCH(\infty) form of the GARCH model. This model can provide varying structures for conditional…
This paper studies computationally and theoretically attractive estimators called the Laplace type estimators (LTE), which include means and quantiles of Quasi-posterior distributions defined as transformations of general…
The Laplace approximation (LA) has been proposed as a method for approximating the marginal likelihood of statistical models with latent variables. However, the approximate maximum likelihood estimators (MLEs) based on the LA are often…
This article develops a random effects quantile regression model for panel data that allows for increased distributional flexibility, multivariate heterogeneity, and time-invariant covariates in situations where mean regression may be…
Strong consistency and asymptotic normality of the Quasi-Maximum Likelihood Estimator (QMLE) are given for a general class of multidimensional causal processes. For particular cases already studied in the literature (for instance univariate…
We link conditional generative modelling to quantile regression. We propose a suitable loss function and derive minimax convergence rates for the associated risk under smoothness assumptions imposed on the conditional distribution. To…
To avoid specification of the error distribution in a regression model, we propose a general nonparametric scale mixture model for the error distribution. For fitting such mixtures, the predictive recursion method is a simple and…
In this paper we propose a multivariate quantile regression framework to forecast Value at Risk (VaR) and Expected Shortfall (ES) of multiple financial assets simultaneously, extending Taylor (2019). We generalize the Multivariate…
We propose a model selection criterion to detect purely causal from purely noncausal models in the framework of quantile autoregressions (QAR). We also present asymptotics for the i.i.d. case with regularly varying distributed innovations…