On Confidence Bands for Quantiles of a Normal Population
- 1 June 1976
- journal article
- research article
- Published by JSTOR in Journal of the American Statistical Association
- Vol. 71 (354) , 417
- https://doi.org/10.2307/2285325
Abstract
Given the general linear regression model , where y is N X 1, X of full rank is N X (q + 1), is (q + 1) X 1, and e is N(0, σ2I), Steinhorst and Bowden [5], using the theory of Roy's maximum root test statistics, set confidence bands for , of the normal population with mean and variance σ2, k being the pth quantile of the standard normal distribution, I fixed or specified but unknown and p known. However, narrower bands may be obtained using the exact test statistic, Student's t. The bands lead to confidence intervals for a known fixed I for which a given component of y, say, , is the pth quantile of the distribution of that component of y, or, conversely, confidence intervals for yp for fixed I.Keywords
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