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Spectral methods have greatly advanced the estimation of latent variable models, generating a sequence of novel and efficient algorithms with strong theoretical guarantees. However, current spectral algorithms are largely restricted to…
In many modern applications, a carefully designed primary study provides individual-level data for interpretable modeling, while summary-level external information is available through black-box, efficient, and nonparametric…
Extending rank-based inference to a multivariate setting such as multiple-output regression or MANOVA with unspecified d-dimensional error density has remained an open problem for more than half a century. None of the many solutions…
Linear regression is a fundamental and popular statistical method. There are various kinds of linear regression, such as mean regression and quantile regression. In this paper, we propose a new one called distribution regression, which…
Multivariate count data are defined as the number of items of different categories issued from sampling within a population, which individuals are grouped into categories. The analysis of multivariate count data is a recurrent and crucial…
In this paper, we study parametric nonlinear regression under the Harris recurrent Markov chain framework. We first consider the nonlinear least squares estimators of the parameters in the homoskedastic case, and establish asymptotic theory…
Extending to dimension 2 and higher the dual univariate concepts of ranks and quantiles has remained an open problem for more than half a century. Based on measure transportation results, a solution has been proposed recently under the name…
Non-causal processes have been drawing attention recently in Macroeconomics and Finance for their ability to display nonlinear behaviors such as asymmetric dynamics, clustering volatility, and local explosiveness. In this paper, we…
The paper considers nonparametric specification tests of quantile curves for a general class of nonstationary processes. Using Bahadur representation and Gaussian approximation results for nonstationary time series, simultaneous confidence…
Modal regression has emerged as a flexible alternative to classical regression models when the conditional mean or median are unable to adequately capture the underlying relation between a response and a predictor variable. This approach is…
Quantifying predictive uncertainty is essential for safe and trustworthy real-world AI deployment. Yet, fully nonparametric estimation of conditional distributions remains challenging for multivariate targets. We propose Tomographic…
Quantile estimation and regression within the Bayesian framework is challenging as the choice of likelihood and prior is not obvious. In this paper, we introduce a novel Bayesian nonparametric method for quantile estimation and regression…
Quantile regression (QR) is a statistical tool for distribution-free estimation of conditional quantiles of a target variable given explanatory features. QR is limited by the assumption that the target distribution is univariate and defined…
Motivated by the problem of nonparametric inference in high level digital image analysis, we introduce a general extrinsic approach for data analysis on Hilbert manifolds with a focus on means of probability distributions on such sample…
Multivariate mixed-type outcomes are difficult to model jointly, and additional complexity arises when both marginal effects and dependence structures vary with a covariate such as age or time. Existing approaches often impose restrictive…
The paper introduces a novel topological method for prediction and modeling for a nonlinear time--series that exhibit recurring patterns. According to the model, global manifold of the reconstructed state--space can be approximated by a few…
Multi-output Gaussian Processes provide principled uncertainty-aware learning of vector-valued fields but are difficult to deploy in large-scale, distributed, and streaming settings due to their computational and centralized nature. This…
Increasing practical interest has been shown in regression problems where the errors, or disturbances, are centred in a way that reflects particular characteristics of the mechanism that generated the data. In economics this occurs in…
As a competitive alternative to least squares regression, quantile regression is popular in analyzing heterogenous data. For quantile regression model specified for one single quantile level $\tau$, major difficulties of semiparametric…
In this article, we introduce parallel-in-time methods for state and parameter estimation in general nonlinear non-Gaussian state-space models using the statistical linear regression and the iterated statistical posterior linearization…