2015/09/14 by Lee H. Dicker, Dicker, Lee H., Murat A. Erdogdu +1 · 1 citation
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #FOS: Mathematics #Statistical Methods and Bayesian Inference #Statistical Methods and Inference #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.1509.04388
openalex publication_date 2015/09/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We derive convenient uniform concentration bounds and finite sample\nmultivariate normal approximation results for quadratic forms, then describe\nsome applications involving variance components estimation in linear\nrandom-effects models. Random-effects models and variance components estimation\nare classical topics in statistics, with a corresponding well-established\nasymptotic theory. However, our finite sample results for quadratic forms\nprovide additional flexibility for easily analyzing random-effects models in\nnon-standard settings, which are becoming more important in modern applications\n(e.g. genomics). For instance, in addition to deriving novel non-asymptotic\nbounds for variance components estimators in classical linear random-effects\nmodels, we provide a concentration bound for variance components estimators in\nlinear models with correlated random-effects. Our general concentration bound\nis a uniform version of the Hanson-Wright inequality. The main normal\napproximation result in the paper is derived using Reinert and R "ollin's\n(2009) embedding technique and multivariate Stein's method with exchangeable\npairs.\n