期刊
STATISTICA SINICA
卷 28, 期 4, 页码 2565-2589出版社
STATISTICA SINICA
DOI: 10.5705/ss.202016.0546
关键词
Confidence intervals; Edgeworth expansion; resampling; second-order correctness
资金
- NSF [DMS-1512084, DMS-1406563, DMS-1309619, DMS-1613112, IIS-1633212, DMS-1127914]
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [1406563] Funding Source: National Science Foundation
We consider inference for the parameters of a linear model when the covariates are random and the relationship between response and covariates is possibly non-linear. Conventional inference methods such as z intervals perform poorly in these cases. We propose a double bootstrap-based calibrated percentile method, perc-cal, as a general-purpose CI method which performs very well relative to alternative methods in challenging situations such as these. The superior performance of perc-cal is demonstrated by a thorough, full-factorial design synthetic data study as well as a data example involving the length of criminal sentences. We also provide theoretical justification for the perc-cal method under mild conditions. The method is implemented in the R package 'perccal', available through CRAN and coded primarily in C++, to make it easier for practitioners to use.
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