Related papers: A Linear Model for Interval-valued Data
Additive regression models are actively researched in the statistical field because of their usefulness in the analysis of responses determined by non-linear relationships with multivariate predictors. In this kind of statistical models,…
We study parameter estimation and asymptotic inference for sparse nonlinear regression. More specifically, we assume the data are given by $y = f( x^\top \beta^* ) + \epsilon$, where $f$ is nonlinear. To recover $\beta^*$, we propose an…
We study partially linear models when the outcome of interest and some of the covariates are observed in two different datasets that cannot be linked. This type of data combination problem arises very frequently in empirical microeconomics.…
Functional data analysis is a fast evolving branch of statistics. Estimation procedures for the popular functional linear model either suffer from lack of robustness or are computationally burdensome. To address these shortcomings, a…
Linear regression on network-linked observations has been an essential tool in modeling the relationship between response and covariates with additional network structures. Previous methods either lack inference tools or rely on restrictive…
If X and Y are real valued random variables such that the first moments of X, Y, and XY exist and the conditional expectation of Y given X is an affine function of X, then the intercept and slope of the conditional expectation equal the…
In different fields of applications including, but not limited to, behavioral, environmental, medical sciences and econometrics, the use of panel data regression models has become increasingly popular as a general framework for making…
In recent years, the modeling and analysis of interval-valued time series have garnered significant attention in the fields of econometrics and statistics. However, the existing literature primarily focuses on regression tasks while…
For the last two decades, high-dimensional data and methods have proliferated throughout the literature. Yet, the classical technique of linear regression has not lost its usefulness in applications. In fact, many high-dimensional…
The linear regression model is widely used in empirical work in Economics, Statistics, and many other disciplines. Researchers often include many covariates in their linear model specification in an attempt to control for confounders. We…
Generalized linear models are flexible tools for the analysis of diverse datasets, but the classical formulation requires that the parametric component is correctly specified and the data contain no atypical observations. To address these…
We propose a novel nonparametric regression method that models complex input-output relationships as the sum of convex and concave components. The method-Identifiable Convex-Concave Nonparametric Least Squares (ICCNLS)-decomposes the target…
Sufficient conditions for the design of a simple class of interval observers for linear impulsive systems subject to minimum and range dwell-time constraints are obtained and formulated in terms of infinite-dimensional linear programs. The…
Aggregation of large databases in a specific format is a frequently used process to make the data easily manageable. Interval-valued data is one of the data types that is generated by such an aggregation process. Using traditional methods…
Regression splines are smooth, flexible, and parsimonious nonparametric function estimators. They are known to be sensitive to knot number and placement, but if assumptions such as monotonicity or convexity may be imposed on the regression…
Linear models are foundational tools in statistics and ubiquitous across the applied sciences. However, conventional statistical inference -- such as $t$-tests and $F$-tests -- are only valid at fixed sample sizes, making them unsuitable…
This paper develops a unified finite-time theory for the ordinary least squares estimation of possibly unstable and even slightly explosive vector autoregressive models under linear restrictions, with the applicable region $\rho(A)\leq…
Regression models are essential for a wide range of real-world applications. However, in practice, target values are not always precisely known; instead, they may be represented as intervals of acceptable values. This challenge has led to…
The panel data regression models have gained increasing attention in different areas of research including but not limited to econometrics, environmental sciences, epidemiology, behavioral and social sciences. However, the presence of…
Concerning bivariate least squares linear regression, the classical approach pursued for functional models in earlier attempts is reviewed using a new formalism in terms of deviation (matrix) traces. Within the framework of classical error…