Title: VALID CONFIDENCE INTERVALS IN REGRESSION AFTER VARIABLE SELECTION
Abstract:We consider a linear regression model with regression parameters (θ 1 ,...,θ p ) and error variance parameter σ 2 . Our aim is to find a confidence interval with minimum coverage probability 1 − α for...We consider a linear regression model with regression parameters (θ 1 ,...,θ p ) and error variance parameter σ 2 . Our aim is to find a confidence interval with minimum coverage probability 1 − α for a parameter of interest θ 1 in the presence of nuisance parameters (θ 2 ,...,θ p ,σ 2 ). We consider two confidence intervals, the first of which is the standard confidence interval for θ 1 with coverage probability 1 − α. The second confidence interval for θ 1 is obtained after a variable selection procedure has been applied to θ p . This interval is chosen to be as short as possible subject to the constraint that it has minimum coverage probability 1 − α. The confidence intervals are compared using a risk function that is defined as a scaled version of the expected length of the confidence interval. We show that, subject to certain conditions including that [(dimension of response vector) − p ] is small, the second confidence interval is preferable to the first when we anticipate (without being certain) that |θ p |/σ is small. This comparison of confidence intervals is shown to be mathematically equivalent to a corresponding comparison of prediction intervals.Read More
Publication Year: 1998
Publication Date: 1998-08-01
Language: en
Type: article
Indexed In: ['crossref']
Access and Citation
Cited By Count: 48
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