A selection problem for a constrained linear regression model

The Optimal Selection for Restricted Linear Models with Average Estimator

“…In other words, the selected weights from -GIC are asymptotically optimal. Moreover, we highlight two new results which enrich the works of Lai and Xie [26]. One is that an estimate of variance is given and the estimate is proved to be consistent.…”

“…. , ∞, the model (4) becomes = which which has been discussed by Lai and Xie [26]. Particularly, if set 1 = ⋅ ⋅ ⋅ = = 1, 1,1 + ⋅ ⋅ ⋅ + ,1 = ⋅ ⋅ ⋅ = 1,∞ + ⋅ ⋅ ⋅ + ,∞ = −1, and 1 + ⋅ ⋅ ⋅ + = 1, the restricted equation (4) turns into (2).…”

“…Since , can be viewed as a series expansion, the identity (3) includes semiparametric models as special form. In fact, the model (3) generalizes the models considered by Lai and Xie [26] and Liang et al [12]. In addition, the parameters and denote, respectively, the proportion of the th required stock and the th alternative stock in a tracking portfolio.…”

“…The literature mentioned above pays more attention to the unconstrained models with independently and identically distributed random errors. Recently, Lai and Xie [26] discussed model selection for constrained models, which were limited to the homoscedastic cases. Instead of using unrestricted models or homoscedastic models, we develop a -class generalized information criterion ( -GIC) to discuss the selecting problems of approximately constrained linear models with dependent errors.…”