Related papers: The Yule-Frisch-Waugh-Lovell Theorem

Quantile regression is a powerful statistical methodology that complements the classical linear regression by examining how covariates influence the location, scale, and shape of the entire response distribution and offering a global view…

The Fr\'echet regression is a useful method for modeling random objects in a general metric space given Euclidean covariates. However, the conventional approach could be sensitive to outlying objects in the sense that the distance from the…

A Yule tree is the result of a branching process with constant birth and death rates. Such a process serves as an instructive null model of many empirical systems, for instance, the evolution of species leading to a phylogenetic tree.…

This paper introduces a flexible framework for the estimation of the conditional tail index of heavy tailed distributions. In this framework, the tail index is computed from an auxiliary linear regression model that facilitates estimation…

The Stochastic Loewner equation, introduced by Schramm, gives us a powerful way to study and classify critical random curves and interfaces in two-dimensional statistical mechanics. New kind of stochastic Loewner equation, called fractional…

In this paper, we resolve a longstanding open statistical problem. The problem is to mathematically confirm Yule's 1926 empirical finding of "nonsense correlation" (\cite{Yule}). We do so by analytically determining the second moment of the…

It is widely known that geographically weighted regression(GWR) is essentially same as varying-coefficient model. In the former research about varying-coefficient model, scholars tend to use multidimensional-kernel-based locally weighted…

Logistic regression involving high-dimensional covariates is a practically important problem. Often the goal is variable selection, i.e., determining which few of the many covariates are associated with the binary response. Unfortunately,…

In this paper we complete our understanding of the role played by the limiting (or residue) function in the context of mod-Gaussian convergence. The question about the probabilistic interpretation of such functions was initially raised by…

The interpretation of coefficients from multivariate linear regression relies on the assumption that the conditional expectation function is linear in the variables. However, in many cases the underlying data generating process is…

Multivariate processes with long-range dependent properties are found in a large number of applications including finance, geophysics and neuroscience. For real data applications, the correlation between time series is crucial. Usual…

High-fidelity (HF) data are often expensive to collect and therefore scarce, making conditional quantiles difficult to estimate accurately. We propose a two-stage, model-agnostic method for multi-fidelity quantile regression. The central…

Adaptive designs dynamically update treatment probabilities using information accumulated during the experiment. Existing theory for causal inference from adaptive experiments primarily assumes the superpopulation framework with independent…

Machine learning has revitalized causal inference by combining flexible models and principled estimators, yet robust benchmarking and evaluation remain challenging with real-world data. In this work, we introduce frengression, a deep…

Causal inference using observational text data is becoming increasingly popular in many research areas. This paper presents the Bayesian Topic Regression (BTR) model that uses both text and numerical information to model an outcome…

A variational principle is developed for fractional kinetics based on the auxiliary-field formalism. It is applied to the Fokker-Planck equation with spatio-temporal fractionality, and a variational solution is obtained with the help of the…

We augment the method of Wooley (2015) by some new ideas and in a series of results, improve his metric bounds on the Weyl sums and the discrepancy of fractional parts of real polynomials with partially prescribed coefficients. We also…

Measuring the correlation (association) between two random variables is one of the important goals in statistical applications. In the literature, the covariance between two random variables is a widely used criterion in measuring the…

Training deep neural networks requires many training samples, but in practice training labels are expensive to obtain and may be of varying quality, as some may be from trusted expert labelers while others might be from heuristics or other…

In this paper, a functional partial quantile regression approach, a quantile regression analog of the functional partial least squares regression, is proposed to estimate the function-on-function linear quantile regression model. A partial…