Confidence Intervals based on Rank Statistics in Linear Models
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Abstract
Consider the linear models of which the distributions of the errors are non-normal. We propose a method based on rank statistics for constructing confidence intervals for the parameters in the linear models. It is found that the proposed confidence intervals have coverage probabilities which are fairly close to the target value. Furthermore when the skewness of the distributions is large, the expected lengths of the proposed confidence intervals are found to be much shorter than those of the percentile bootstrap confidence intervals, and the classical confidence intervals which are derived by assuming that the errors are normally distributed.
Pertimbangkan model linear dengan ralat yang bertaburan tak normal. Kita mencadangkan satu kaedah berasaskan statistik pangkat untuk membina selang keyakinan bagi parameter dalam model linear. Didapati kaedah yang dicadangkan mempunyai kebarangkalian liputan yang menghampiri nilai sasaran. Tambahan pula, apabila nilai kepincangan taburan adalah besar, kaedah yang dicadangkan menghasilkan selang keyakinan yang mempunyai panjang jangkaan yang jauh lebih pendek daripada selang keyakinan yang berdasarkan kaedah bootstrap persentil, dan kaedah klasikal yang mengandaikan bahawa taburan ralatnya adalah normal.
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