For a random sample of size n from general linear model, $Y_i= heta(X_i)+varepsilon_i,;let Y_{in}$ denote the ith oder statistics of the Y sample values. The X-value associated with $Y_{in}$ is denoted by $X_{[in]}$ and is called the concomitant of ith order statistics. The estimator of the location of a maximum of a regression function, $ heta$($chi$), was proposed by (equation omitted) and was found the convergence rate of it under certain weak assumptions on $ heta$. We will discuss the asymptotic distributions of both $ heta(X_{〔n-r+1〕}$) and (equation omitted) when r is fixed as nolongrightarrow$infty$(i.e. extreme case) on the basis of the theorem of the concomitants of order statistics. And the will investigate the asymptotic behavior of Max｛$ heta$( $X_{〔n-r+1:n〕/}$ ), . , $ heta$( $X_{〔n:n〕}$)｝as an estimator for the peak of a regression function.