Communications for Statistical Applications and Methods

  • 제5권3호
  • /
  • Pages.855-868
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  • 1998
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  • 2287-7843(pISSN)
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  • 2383-4757(eISSN)
한국통계학회 (The Korean Statistical Society)
권호 표지

Distribution of the Estimator for Peak of a Regression Function Using the Concomitants of Extreme Oder Statistics

  • Kim, S.H (Department of Statistics and Information, Anyang University) ;
  • Kim, T.S. (Department of Statistics, Won-Kwang University)
  • 발행 : 1998.12.01
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초록

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$(i.e. extreme case) on the basis of the theorem of the concomitants of order statistics. And the will investigate the asymptotic behavior of Max｛$\theta$( $X_{〔n-r+1:n〕/}$ ), . , $\theta$( $X_{〔n:n〕}$)｝as an estimator for the peak of a regression function.

키워드

참고문헌

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