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Collinearity and near-collinearity of predictors cause difficulties when doing regression. In these cases, variable selection becomes untenable because of mathematical issues concerning the existence and numerical stability of the…
We provide a unified approach to a method of estimation of the regression parameter in balanced linear models with a structured covariance matrix that combines a high breakdown point and bounded influence with high asymptotic efficiency at…
Concerning bivariate least squares linear regression, the classical results obtained for extreme structural models in earlier attempts are reviewed using a new formalism in terms of deviation (matrix) traces which, for homoscedastic data,…
This paper studies a very flexible model that can be used widely to analyze the relation between a response and multiple covariates. The model is nonparametric, yet renders easy interpretation for the effects of the covariates. The model…
Classical regression analysis relates the expectation of a response variable to a linear combination of explanatory variables. In this article, we propose a covariance regression model that parameterizes the covariance matrix of a…
The properties of the normal distribution under linear transformation, as well the easy way to compute the covariance matrix of marginals and conditionals, offer a unique opportunity to get an insight about several aspects of uncertainties…
We discuss a class of difference-based estimators for the autocovariance in nonparametric regression when the signal is discontinuous (change-point regression), possibly highly fluctuating, and the errors form a stationary $m$-dependent…
Extensions of previous linear regression models for interval data are presented. A more flexible simple linear model is formalized. The new model may express cross-relationships between mid-points and spreads of the interval data in a…
Ordinary least squares (OLS) linear regression is one of the most basic statistical techniques for data analysis. In the main stream literature and the statistical education, the study of linear regression is typically restricted to the…
In a recent paper Noh et al. (2013) proposed a new semiparametric estimate of a regression function with a multivariate predictor, which is based on a specification of the dependence structure between the predictor and the response by means…
Statistical inference on the explained variation of an outcome by a set of covariates is of particular interest in practice. When the covariates are of moderate to high-dimension and the effects are not sparse, several approaches have been…
We provide finite-sample distribution approximations, that are uniform in the parameter, for inference in linear mixed models. Focus is on variances and covariances of random effects in cases where existing theory fails because their…
Linear regression is a data analysis technique, which is categorized as supervised learning. By utilizing known data, we can predict unknown data. Recently, researchers have explored the use of quantum annealing (QA) to perform linear…
When we interpret linear regression as estimating causal effects justified by quasi-experimental treatment variation, what do we mean? This paper formalizes a minimal criterion for quasi-experimental interpretation and characterizes its…
This paper studies the inference of the regression coefficient matrix under multivariate response linear regressions in the presence of hidden variables. A novel procedure for constructing confidence intervals of entries of the coefficient…
Linear regression is a fundamental modeling tool in statistics and related fields. In this paper, we study an important variant of linear regression in which the predictor-response pairs are partially mismatched. We use an optimization…
When data contains measurement errors, it is necessary to make assumptions relating the observed, erroneous data to the unobserved true phenomena of interest. These assumptions should be justifiable on substantive grounds, but are often…
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…
The paper introduces a new estimation method for the standard linear regression model. The procedure is not driven by the optimisation of any objective function rather, it is a simple weighted average of slopes from observation pairs. The…
In a multiple linear regression model, the algebraic formula of the decomposition theorem explains the relationship between the univariate regression coefficient and partial regression coefficient using geometry. It was found that…