Bias and convergence rate of the coverage probability of prediction intervals in Box–Cox transformed linear models

We study the asymptotic bias and convergence rate of the coverage probability of a prediction interval in a Box–Cox transformed linear model. The leading terms in the coverage probability are obtained both when the transformation parameter is known and when it is estimated. Analytical and simulation...

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Bibliographic Details
Published in:Journal of statistical planning and inference 2006-10, Vol.136 (10), p.3614-3624
Main Authors: Cho, Kwanho, Loh, Wei-Yin
Format: Article
Language:English
Subjects:
Acceleration of convergence
Asymptotic bias
Exact sciences and technology
General topics
Inference from stochastic processes
time series analysis
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Probability and statistics
Probability theory and stochastic processes
Regression
Sciences and techniques of general use
Statistics
Stochastic processes
Transformation
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Summary:We study the asymptotic bias and convergence rate of the coverage probability of a prediction interval in a Box–Cox transformed linear model. The leading terms in the coverage probability are obtained both when the transformation parameter is known and when it is estimated. Analytical and simulation results show that the cost of not knowing the transformation can be large in terms of coverage probability and asymptotic bias.
ISSN:0378-3758
1873-1171
DOI:10.1016/j.jspi.2005.03.004