CONSTRUCTION OF CONFIDENCE BANDS FOR SIMPLE LINEAR REGRESSION OVER BOUNDED INTERVALS

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  • Fujisawa Masaki
    Clinical Control Group, Research & Development Division, Grelan Pharmaceutical Co., LTD
  • Baba Mitsumasa
    Biometry Data Management, Medical Development, Research & Development
  • Sakamoto Wataru
    Department Division of Informatics and Mathematical Science, Graduate School of Engineering Sciences, Osaka University
  • Goto Masashi
    Department Division of Informatics and Mathematical Science, Graduate School of Engineering Sciences, Osaka University

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  • 有限区間における回帰直線の信頼帯の構成
  • ユウゲン クカン ニ オケル カイキ チョクセン ノ シンライタイ ノ コウセイ

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Abstract

In this article, we discuss methods to construct confidence bands for regression function, especially to construct uniform width-confidence bands and trapezoidal confidence bands in a finite interval of interest. With case studies and numerical experiments, we examined the coverage probability and the efficiency (area ratio) of these confidence bands. From a viewpoint of the coverage probability, it is reasonable to use the uniform width- confidence bands (Gafarian bands) and trapezoidal confidence bands (Bowden-Graybill bands) for the finite interval of interest, rather than to use the Working-Hotelling bands. In particular, the use of these confidence bands can be emphasized when a length of the interval of interest is smaller than that of the observation interval. Moreover, from the examination about efficiency, it is strongly recommended to use the trapezoidal confidence bands when the interval of interest is near the relative ends of the observation interval.

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