2010/08/25 by Davide Farchione, Paul Kabaila, Farchione, Davide +1
Computer Science · Mathematics · #Advanced Statistical Methods and Models #FOS: Computer and information sciences #Face and Expression Recognition #Methodology (stat.ME) #Statistical Methods and Bayesian Inference #Statistical Methods and Inference
paper · pdf · doi:10.48550/arxiv.1008.4203
openalex publication_date 2010/08/25 · openalex created_date 2022/09/05 · openalex updated_date 2026/07/28
Hard thresholding, LASSO , adaptive LASSO and SCAD point estimators have been\nsuggested for use in the linear regression context when most of the components\nof the regression parameter vector are believed to be zero, a sparsity type of\nassumption. Potscher and Schneider, 2010, Electronic Journal of Statistics,\nhave considered the properties of fixed-width confidence intervals that include\none of these point estimators (for all possible data values). They consider a\nnormal linear regression model with orthogonal regressors and show that these\nconfidence intervals are longer than the standard confidence interval (based on\nthe maximum likelihood estimator) when the tuning parameter for these point\nestimators is chosen to lead to either conservative or consistent model\nselection. We extend this analysis to the case of variable-width confidence\nintervals that include one of these point estimators (for all possible data\nvalues). In consonance with these findings of Potscher and Schneider, we find\nthat these confidence intervals perform poorly by comparison with the standard\nconfidence interval, when the tuning parameter for these point estimators is\nchosen to lead to consistent model selection. However, when the tuning\nparameter for these point estimators is chosen to lead to conservative model\nselection, our conclusions differ from those of Potscher and Schneider. We\nconsider the variable-width confidence intervals of Farchione and Kabaila,\n2008, Statistics & Probability Letters, which have advantages over the standard\nconfidence interval in the context that there is a belief in a sparsity type of\nassumption. These variable-width confidence intervals are shown to include the\nhard thresholding, LASSO, adaptive LASSO and SCAD estimators (for all possible\ndata values) provided that the tuning parameters for these estimators are\nchosen to belong to an appropriate interval.\n