Asymptotic for Lasso Estimator in High-Dimensional Repeated Measurements Model

Abstract In this paper, we propose high-dimensional repeated measurements model and using the Bridge estimator as penalized method that minimizes the residual sum of squares plus penalty term ∑|θj|γ. After that, under appropriate conditions, we discuss the consistency and asymptotic behavior of lasso estimator whenγ= 1 as especial case and also study the consistency and limiting distribution of the Bridge estimators whenγ< 1 andγ> 1. Moreover, we discuss the asymptotic of estimators by using small parameter and local asymptotic. In other words, we discuss the asymptotic behavior in a triangular array of observations.