Faraldo Roca, P.; González Manteiga, Wenceslao Efficiency of a new class of linear regression estimates obtained by preliminary nonparametric estimation. (English) Zbl 0632.62064 New perspectives in theoretical and applied statistics, Sel. Pap. 3rd Int. Meet. Stat., Bilbao/Spain 1986, 229-242 (1987). [For the entire collection see Zbl 0608.00013.] In this paper, a new class of estimates for the parameters \(\theta_ 1\) and \(\theta_ 2\) of the linear regression model \(Y=\alpha (X)+\eta =\theta_ 1+\theta_ 2X+\eta\), where X is also a random variable, is obtained by minimizing with respect to \(\theta_ 1\) and \(\theta_ 2\) a functional distance between the nonparametric estimation and the line \(\alpha\). Consistency and asymptotic normality of such estimates are derived. It is shown that the new estimates for some special cases can be more efficient than the classical least squares estimates. Reviewer: Wu Qiguang Cited in 4 Documents MSC: 62J05 Linear regression; mixed models 62G05 Nonparametric estimation Keywords:mean-square error; efficiency; Consistency; asymptotic normality; least squares estimates Citations:Zbl 0608.00013 PDFBibTeX XML