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Permanent link (DOI): https://doi.org/10.7939/R3542JN91

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A new distribution-free approach to constructing the confidence region for multiple parameters Open Access

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Author or creator
Hu, Zhiqiu
Yang, Rong-Cai
Additional contributors
Subject/Keyword
Heart Rate
Confidence Intervals
Oxygen
Ellipses
Simulation and Modeling
Normal Distribution
Autocorrelation
Statistical Inference
Type of item
Journal Article (Published)
Language
English
Place
Time
Description
Construction of confidence intervals or regions is an important part of statistical inference. The usual approach to constructing a confidence interval for a single parameter or confidence region for two or more parameters requires that the distribution of estimated parameters is known or can be assumed. In reality, the sampling distributions of parameters of biological importance are often unknown or difficult to be characterized. Distribution-free nonparametric resampling methods such as bootstrapping and permutation have been widely used to construct the confidence interval for a single parameter. There are also several parametric (ellipse) and nonparametric (convex hull peeling, bagplot and HPDregionplot) methods available for constructing confidence regions for two or more parameters. However, these methods have some key deficiencies including biased estimation of the true coverage rate, failure to account for the shape of the distribution inherent in the data and difficulty to implement. The purpose of this paper is to develop a new distribution-free method for constructing the confidence region that is based only on a few basic geometrical principles and accounts for the actual shape of the distribution inherent in the real data. The new method is implemented in an R package, distfree.cr/R. The statistical properties of the new method are evaluated and compared with those of the other methods through Monte Carlo simulation. Our new method outperforms the other methods regardless of whether the samples are taken from normal or non-normal bivariate distributions. In addition, the superiority of our method is consistent across different sample sizes and different levels of correlation between the two variables. We also analyze three biological data sets to illustrate the use of our new method for genomics and other biological researches.
Date created
2013
DOI
doi:10.7939/R3542JN91
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Attribution 4.0 International
Citation for previous publication
Hu, Z., & Yang, R. -C. (2013). A new distribution-free approach to constructing the confidence region for multiple parameters. PLoS ONE, 8(12), e81179 [13 pages].  http://dx.doi.org/10.1371/journal.pone.0081179

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