Regression rank scores in nonlinear models
Abstract
Description
Consider the nonlinear regression model $Y_i=g({\bf x}_i,\boldmath $θ$)+e_i,\quad i=1,...,n$(1) with ${\bf x}_i\in \mathbb{R}^k,$ $\boldmathθ=(θ_0,θ_1,...,θ_p)^{\prime}\in \boldmath $Θ$$ (compact in $\mathbb{R}^{p+1}$), where $g({\bf x},\boldmath $θ$)=θ_0+\tilde{g}({\bf x},θ_1,...,θ_p)$ is continuous, twice differentiable in $\boldmath $θ$$ and monotone in components of $\boldmath $θ$$. Following Gutenbrunner and Jurečková (1992) and Jurečková and Procházka (1994), we introduce regression rank scores for model (1), and prove their asymptotic properties under some regularity conditions. As an application, we propose some tests in nonlinear regression models with nuisance parameters.
Published in at http://dx.doi.org/10.1214/193940307000000121 the IMS Collections (http://www.imstat.org/publications/imscollections.htm) by the Institute of Mathematical Statistics (http://www.imstat.org)
Published in at http://dx.doi.org/10.1214/193940307000000121 the IMS Collections (http://www.imstat.org/publications/imscollections.htm) by the Institute of Mathematical Statistics (http://www.imstat.org)