Efficient estimation strategies for a partially linear model

The objective of this dissertation was to address the problem of estimating regression coefficients for both univariate and multivariate partially linear models in the presence of uncertain prior information. We improved estimation strategies using linear shrinkage, pretest, shrinkage pretest, shrinkage, and positive-part shrinkage methods, which efficiently combine the full model and submodel estimators optimally. The asymptotic properties of the proposed estimators were examined. We conducted Monte Carlo simulation studies to assess the performance of proposed estimators, and compared with those of penalty estimators including LASSO and aLASSO. The proposed estimation strategies were applied to real datasets to investigate their usefulness.A univariate partially linear model was studied in Chapter 3. In this model, the nonparametric component was estimated using smoothing splines method. The asymptotic distributional bias and risk of the proposed estimators were investigated. The asymptotic results show the superiority of proposed estimation strategies. Monte Carlo simulations were conducted for comparing the estimators in context of both low-dimensional and high-dimensional data. Two data examples were also presented. The numerical results supported those from the theoretical results.In Chapter 4, efficient estimation strategies in a multivariate partially linear model have been discussed. In this model, the nonparametric component was estimated using kernel smoothing method. The asymptotic properties of the proposed estimators were examined. We numerically compared their performance to those of penalty estimators using simulation studies and real-world data examples. Regardless of the accuracy of the information, the proposed estimators were found to be more efficient than the full model estimator.