Abstract
ABSTRACTIn this paper, we consider estimation techniques based on ridge regression when the matrix appears to be ill-conditioned in the partially linear model using kernel smoothing. Furthermore, we consider that the coefficients can be partitioned as where is the coefficient vector for main effects, and is the vector for ‘nuisance’ effects. We are essentially interested in the estimation of when it is reasonable to suspect that is close to zero. We suggest ridge pretest, ridge shrinkage and ridge positive shrinkage estimators for the above semi-parametric model, and compare its performance with some penalty estimators. In particular, suitability of estimating the nonparametric component based on the kernel smoothing basis function is also explored. Monte Carlo simulation study is used to compare the relative efficiency of proposed estimators, and a real data example is presented to illustrate the usefulness of the suggested methods. Moreover, the asymptotic properties of the proposed estimators are obtained.
Published Version
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