Accurate confidence intervals in regression analyses of non-normal data |
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Authors: | Robert J Boik |
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Institution: | (1) Department of Mathematical Sciences, Montana State University, Bozeman, MT 59717-2400, USA |
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Abstract: | A linear model in which random errors are distributed independently and identically according to an arbitrary continuous distribution
is assumed. Second- and third-order accurate confidence intervals for regression parameters are constructed from Charlier
differential series expansions of approximately pivotal quantities around Student’s t distribution. Simulation verifies that small sample performance of the intervals surpasses that of conventional asymptotic
intervals and equals or surpasses that of bootstrap percentile-t and bootstrap percentile-|t| intervals under mild to marked departure from normality. |
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Keywords: | Bootstrap Charlier differential series Cornish-Fisher transformation Edgeworth expansion Kurtosis One-sample t Skewness |
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