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Least squares linear regression is one of the oldest and widely used data analysis tools. Although the theoretical analysis of the ordinary least squares (OLS) estimator is as old, several fundamental questions are yet to be answered.…

Statistics Theory · Mathematics 2019-10-16 Arun K. Kuchibhotla , Lawrence D. Brown , Andreas Buja , Junhui Cai

Intensive longitudinal (IL) data are increasingly prevalent in psychological science, coinciding with technological advancements that make it simple to deploy study designs such as daily diary and ecological momentary assessments. IL data…

Methodology · Statistics 2025-01-08 Teague R. Henry , Lindley R. Slipetz , Ami Falk , Jiaxing Qiu , Meng Chen

We present an exploratory restricted latent class model where response data is for a single time point, polytomous, and differing across items, and where latent classes reflect a multi-attribute state where each attribute is ordinal. Our…

Methodology · Statistics 2026-03-10 Eric Alan Wayman , Steven Andrew Culpepper , Jeff Douglas , Jesse Bowers

How should researchers analyze randomized experiments in which the main outcome is latent and measured in multiple ways but each measure contains some degree of error? We first identify a critical study-specific noncomparability problem in…

Econometrics · Economics 2026-01-13 Jiawei Fu , Donald P. Green

This paper is dedicated to a robust ordinal method for learning the preferences of a decision maker between subsets. The decision model, derived from Fishburn and LaValle (1996) and whose parameters we learn, is general enough to be…

Artificial Intelligence · Computer Science 2023-08-08 Hugo Gilbert , Mohamed Ouaguenouni , Meltem Ozturk , Olivier Spanjaard

Longitudinal data are important in numerous fields, such as healthcare, sociology and seismology, but real-world datasets present notable challenges for practitioners because they can be high-dimensional, contain structured missingness…

Machine Learning · Computer Science 2024-07-01 Maksim Sinelnikov , Manuel Haussmann , Harri Lähdesmäki

The main object of investigation in this paper is a very general regression model in optional setting - when an observed process is an optional semimartingale depending on an unknown parameter. It is well-known that statistical data may…

Statistics Theory · Mathematics 2021-03-16 Mohamed Abdelghani , Alexander Melnikov , Andrey Pak

Data on rates, percentages or proportions arise frequently in many different applied disciplines like medical biology, health care, psychology and several others. In this paper, we develop a robust inference procedure for the beta…

Methodology · Statistics 2018-01-16 Abhik Ghosh

In supervised learning, we typically leverage a fully labeled dataset to design methods for function estimation or prediction. In many practical situations, we are able to obtain alternative feedback, possibly at a low cost. A broad goal is…

Machine Learning · Statistics 2020-10-27 Yichong Xu , Sivaraman Balakrishnan , Aarti Singh , Artur Dubrawski

In biomedical studies, researchers are often interested in assessing the association between one or more ordinal explanatory variables and an outcome variable, at the same time adjusting for covariates of any type. The outcome variable may…

Methodology · Statistics 2023-04-17 Kaspar Rufibach

The linear regression model is widely used in the biomedical and social sciences as well as in policy and business research to adjust for covariates and estimate the average effects of treatments. Behind every causal inference endeavor…

Methodology · Statistics 2024-04-23 Ambarish Chattopadhyay , Noah Greifer , Jose R. Zubizarreta

Applied work often studies the effect of a binary variable ("treatment") using linear models with additive effects. I study the interpretation of the OLS estimands in such models when treatment effects are heterogeneous. I show that the…

Econometrics · Economics 2020-05-21 Tymon Słoczyński

The aim of ordinal classification is to predict the ordered labels of the output from a set of observed inputs. Interval-valued data refers to data in the form of intervals. For the first time, interval-valued data and interval-valued…

Methodology · Statistics 2023-11-06 Aleix Alcacer , Marina Martínez-Garcia , Irene Epifanio

In data analysis, latent variables play a central role because they help provide powerful insights into a wide variety of phenomena, ranging from biological to human sciences. The latent tree model, a particular type of probabilistic…

Machine Learning · Computer Science 2014-02-05 Raphaël Mourad , Christine Sinoquet , Nevin L. Zhang , Tengfei Liu , Philippe Leray

In complex survey data, each sampled observation has assigned a sampling weight, indicating the number of units that it represents in the population. Whether sampling weights should or not be considered in the estimation process of model…

Methodology · Statistics 2024-09-20 Amaia Iparragirre , Irantzu Barrio , Jorge Aramendi , Inmaculada Arostegui

The standard linear and logistic regression models assume that the response variables are independent, but share the same linear relationship to their corresponding vectors of covariates. The assumption that the response variables are…

Machine Learning · Computer Science 2019-10-09 Constantinos Daskalakis , Nishanth Dikkala , Ioannis Panageas

In many applications, particularly in the natural sciences, the available high-dimensional set of features may contain variables that are not correlated with the response under consideration. Such irrelevant features can, in certain cases,…

Statistics Theory · Mathematics 2025-07-28 Gianluca Finocchio , Tatyana Krivobokova

A common problem in health research is that we have a large database with many variables measured on a large number of individuals. We are interested in measuring additional variables on a subsample; these measurements may be newly…

Methodology · Statistics 2022-03-22 Thomas Lumley , Tong Chen

The recent wide adoption of Electronic Medical Records (EMR) presents great opportunities and challenges for data mining. The EMR data is largely temporal, often noisy, irregular and high dimensional. This paper constructs a novel ordinal…

Applications · Statistics 2014-07-24 Truyen Tran , Dinh Phung , Wei Luo , Svetha Venkatesh

Ordinal regression with anchored reference samples (ORARS) has been proposed for predicting the subjective Mean Opinion Score (MOS) of input stimuli automatically. The ORARS addresses the MOS prediction problem by pairing a test sample with…

Machine Learning · Computer Science 2022-07-07 Bin Su , Shaoguang Mao , Frank Soong , Zhiyong Wu