Related papers: Wasserstein multivariate auto-regressive models fo…
Data consisting of time-indexed distributions of cross-sectional or intraday returns have been extensively studied in finance, and provide one example in which the data atoms consist of serially dependent probability distributions.…
The problem of modeling the relationship between univariate distributions and one or more explanatory variables has found increasing interest. Traditional functional data methods cannot be applied directly to distributional data because of…
Distribution data refers to a data set where each sample is represented as a probability distribution, a subject area receiving burgeoning interest in the field of statistics. Although several studies have developed…
The analysis of samples of random objects that do not lie in a vector space is gaining increasing attention in statistics. An important class of such object data is univariate probability measures defined on the real line. Adopting the…
We formulate and solve a regression problem with time-stamped distributional data. Distributions are considered as points in the Wasserstein space of probability measures, metrized by the 2-Wasserstein metric, and may represent images,…
This paper considers the problem of regression over distributions, which is becoming increasingly important in machine learning. Existing approaches often ignore the geometry of the probability space or are computationally expensive. To…
Series of univariate distributions indexed by equally spaced time points are ubiquitous in applications and their analysis constitutes one of the challenges of the emerging field of distributional data analysis. To quantify such…
We study distribution-on-distribution regression problems in which a response distribution depends on multiple distributional predictors. Such settings arise naturally in applications where the outcome distribution is driven by several…
Wasserstein autoregression provides a robust framework for modeling serial dependence among probability distributions, with wide-ranging applications in economics, finance, and climate science. In this paper, we develop portmanteau-type…
In this work we study systems consisting of a group of moving particles. In such systems, often some important parameters are unknown and have to be estimated from observed data. Such parameter estimation problems can often be solved via a…
We study the problem of estimating a sequence of evolving probability distributions from historical data, where the underlying distribution changes over time in a nonstationary and nonparametric manner. To capture gradual changes, we…
While statistical modeling of distributional data has gained increased attention, the case of multivariate distributions has been somewhat neglected despite its relevance in various applications. This is because the Wasserstein distance,…
Motivated by the application to German interest rates, we propose a timevarying autoregressive model for short and long term prediction of time series that exhibit a temporary non-stationary behavior but are assumed to mean revert in the…
Many studies have been conducted on flows of probability measures, often in terms of gradient flows. We utilize a generalized notion of derivatives with respect to time to model the instantaneous evolution of empirically observed…
Missing data can significantly hamper standard time series analysis, yet they occur frequently in applications. In this paper, we introduce temporal Wasserstein imputation, a novel method for imputing missing data in time series. Unlike…
In this paper I present a new approach for regression of time series using their own samples. This is a celebrated problem known as Auto-Regression. Dealing with outlier or missed samples in a time series makes the problem of estimation…
A class of multivariate periodic autoregressive models is proposed where coupling between time series is achieved through linear mean functions. Various response distributions with quadratic mean-variance relationships fit into the…
Contemporary time series data often feature objects connected by a social network that naturally induces temporal dependence involving connected neighbours. The network vector autoregressive model is useful for describing the influence of…
In this paper, we propose a new and unified approach for nonparametric regression and conditional distribution learning. Our approach simultaneously estimates a regression function and a conditional generator using a generative learning…
This paper develops computationally feasible methods for estimating random effects models in the context of regression modelling of multiple independent time series of discrete valued counts in which there is serial dependence. Given…