Moment convergence of regularized least-squares estimator for linear regression model

The Global COE Program Mathematics-for-Industry Education & Research HubグローバルCOEプログラム「マス･フォア･インダストリ教育研究拠点」In this paper we study the uniform tail-probability estimates of a regularized least-squares estimator for the linear regression model, by making use of the polynomial type large deviation inequality for the associated statistical random fields, which may not be locally asymptotically quadratic. Our results provide a measure of rate of consistency in variable selection in sparse estimation, which in particular enable us to verify various arguments requiring convergence of moments of estimator-dependent statistics, such as the expected maximum-likelihood for AIC-type and many other moment based model assessment procedure including the C_<p>-type