%0 Generic %1 dicker2015flexible %A Dicker, Lee H. %A Erdogdu, Murat A. %D 2015 %K distributions quadratic-forms statistics %T Flexible results for quadratic forms with applications to variance components estimation %U http://arxiv.org/abs/1509.04388 %X We derive convenient uniform concentration bounds and finite sample multivariate normal approximation results for quadratic forms, then describe some applications involving variance components estimation in linear random-effects models. Random-effects models and variance components estimation are classical topics in statistics, with a corresponding well-established asymptotic theory. However, our finite sample results for quadratic forms provide additional flexibility for easily analyzing random-effects models in non-standard settings, which are becoming more important in modern applications (e.g. genomics). For instance, in addition to deriving novel non-asymptotic bounds for variance components estimators in classical linear random-effects models, we provide a concentration bound for variance components estimators in linear models with correlated random-effects. Our general concentration bound is a uniform version of the Hanson-Wright inequality. The main normal approximation result in the paper is derived using Reinert and Röllin's (2009) embedding technique and multivariate Stein's method with exchangeable pairs.

@misc{dicker2015flexible, abstract = {We derive convenient uniform concentration bounds and finite sample multivariate normal approximation results for quadratic forms, then describe some applications involving variance components estimation in linear random-effects models. Random-effects models and variance components estimation are classical topics in statistics, with a corresponding well-established asymptotic theory. However, our finite sample results for quadratic forms provide additional flexibility for easily analyzing random-effects models in non-standard settings, which are becoming more important in modern applications (e.g. genomics). For instance, in addition to deriving novel non-asymptotic bounds for variance components estimators in classical linear random-effects models, we provide a concentration bound for variance components estimators in linear models with correlated random-effects. Our general concentration bound is a uniform version of the Hanson-Wright inequality. The main normal approximation result in the paper is derived using Reinert and R\"{o}llin's (2009) embedding technique and multivariate Stein's method with exchangeable pairs.}, added-at = {2015-12-23T19:48:09.000+0100}, author = {Dicker, Lee H. and Erdogdu, Murat A.}, biburl = {https://www.bibsonomy.org/bibtex/260b235c7b3662028a26c2f261a48f7f2/shabbychef}, description = {Flexible results for quadratic forms with applications to variance components estimation}, interhash = {5e09316b3486d20fd0ee605e0ce364bc}, intrahash = {60b235c7b3662028a26c2f261a48f7f2}, keywords = {distributions quadratic-forms statistics}, note = {cite arxiv:1509.04388}, timestamp = {2015-12-23T19:48:09.000+0100}, title = {Flexible results for quadratic forms with applications to variance components estimation}, url = {http://arxiv.org/abs/1509.04388}, year = 2015 }