Due to advances in technologies, modern statistical studies often encounter linear models with high-dimension, where the number of explanatory variables is larger than the sample size. Estimation in these high-dimensional problems with deterministic covariates or designs is very different from those in the case of random covariates, due to the identifiability of the high-dimensional semiparametric regression parameters. In this paper, we consider ridge estimators and propose preliminary test, shrinkage and its positive rule ridge estimators in the restricted semiparametric regression model when the errors are dependent under a multicollinear setting, in high-dimension. The asymptotic risk expressions in addition to biases are exactly derived for the estimators under study. For our proposal, a real data analysis about production of vitamin B2 and a Monté–Carlo simulation study are considered to illustrate the efficiency of the proposed estimators. In this regard, kernel smoothing and cross-validation methods for estimating the optimum ridge parameter and nonparametric function are used.

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