Efficiency of a Liu-type estimator in semiparametric regression models

The relative efficiency of Liu-type estimator in a partially linear model

“…. ; t n Þ is an n  n positive-definite smoother matrix from univariate cubic spline smoothing [7]. Consider the following model y ¼Xb þẽ; ð2:2Þ In this section, we will give the comparison of the Liu-type estimatorb p ðk; dÞ with two-step estimatorb p in the mean squared error (MSE) sense.…”

“…Hu [6] used two-step way and introduced a ridge estimators for the partially linear model. Duran et al [7] also discussed the two-step method. The main thought of two steps estimation is the following: the first step, f ðt; bÞ is defined with supposition where b is assumed to be known; the second step, the estimator of parametric b is attained by a least-squares method; Then we may obtainf ðt;bÞ.…”

Quasi-minimax estimation in the partial linear model

“…Such as: Engle et al [2] presented the spline methods, Speckman [3] proposed the kernel method, Chen [4] and Robinson [5] presented the piecewise polynomials method. Hu [6] used the two-step estimation for ridge estimation, Duran et al [7] used the two-step estimator for Liu estimation and Wu [8] used the two-step estimation for two-parameter estimation.…”

Restricted difference-based Liu estimator in partially linear model

“…If X ′ X is ill-conditioned with a large condition number a Liu regression estimator can be used to estimate β (see e.g. [1][2][3][4][5][6][7]). In this paper, we will examine a biased estimation techniques to be followed when the matrix X ′ X appears to be ill-conditioned in the partial linear model.…”