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同时置信带对模型误设的稳健性AI 解读

Confidence bands for the simple linear model are examined to assess their degrees of robustness to departures from the model. All calculations are made under an interval constraint on the range of interest for the predictor variable. The true model is taken to be a quadratic polynomial, and departure from the linear case is considered in terms of increasing magnitude of a curvature parameter. Proposed measures of robustness include the actual coverage probability under the…

简单线性回归置信带的平均宽度最优性AI 解读

The problem of constructing optimal confidence bands for a simple linear regression over the whole real line is considered. Optimality is defined as minimization of the average width of the bands weighted by a normalized function. This weight function is presented as an indicator of experimental interest in the varying width of the band. A comparison between the commonly seen hyperbolic bands and segmented-line bands is presented.

简单线性回归中的可容许与最优置信带AI 解读

A framework is presented for deciding among functional forms when constructing confidence bands in simple linear regression. Using the concept of tautness, definitions of admissibility and completeness are developed. These lead to a characterization of a minimal complete class of band forms. A type of average width optimality within this class is briefly discussed.