Article

A Linear Algebraic Proof of the Gauss-Markov Theorem Under Generalized Conditions: Theory and Empirical Application to Clustered Clinical Data

2026-05-20

Abstract excerpt

The Gauss-Markov Theorem is central to linear statistical inference, assuring that Ordinary Least Squares (OLS) is the Best Linear Unbiased Estimator (BLUE) under the classical assumptions. But textbook proofs typically involve two assumptions - column full rank of the design matrix and spherical error covariance - that are often violated in practice. In this paper, we provide a single unified proof encompassing b...

Topics

Open a Topic to create a Post that cites this publication.

Identifiers and source

Literature Corpus work: 15baa213-9b29-5bb0-a0c1-52ed2c8d24ea
DOI: 10.20944/preprints202605.1372.v1

Open publication

Related research

Semantic proximity does not establish scientific evidence.

Click a neighbor to travelStep 1 · 12 closest

A Linear Algebraic Proof of the Gauss-Markov Theorem Under Generalized Conditions: Theory and Empirical Application to Clustered Clinical DataDOI 10.20944/preprints202605.1372.v1Read

Bridging Classical Statistics and Modern Data Analysis: A Comprehensive Survey of Generalized Linear ModelsSemantic proximity Read

Generalization of the minimum covariance determinant algorithm for categorical and mixed data typesSemantic proximity Read

A Unified Form of Batch Harmonization Equation for Normative Modeling: A Location–Scale FrameworkSemantic proximity Read

Adaptive predictor-set linear model: an imputation-free method for linear regression prediction on datasets with missing valuesSemantic proximity Read

Generalized Mixed Modeling in Massive Electronic Health Record Databases: What is a Healthy Serum Potassium?Semantic proximity Read

Checking the Assumptions of Your Statistical Model Without Getting ParanoidSemantic proximity Read

Sociodemographic Predictors of Consent: A Protocol and Statistical Analysis Plan for a Nested Observational Study of Canadian Sites in the REVISE TrialSemantic proximity Read

Penalized generalized estimating equations for relative risk regression with applications to brain lesion dataSemantic proximity Read

Shift-Aware Sparse Kronecker Tensor ClassificationSemantic proximity Read

Covariate Assisted Principal Regression for Covariance Matrix OutcomesSemantic proximity Read

A Zero-Inflated Spatial Gamma Process Model With Applications to Disease MappingSemantic proximity Read

Non-Gaussian Normative Modelling With Hierarchical Bayesian RegressionSemantic proximity Read