Confidence bands in non‐parametric errors‐in‐variables regression

• Published in: Journal of the Royal Statistical Society. Series B, Statistical methodology Vol. 77; no. 1; pp. 149 - 169
• Main Authors: Delaigle, Aurore, Hall, Peter, Jamshidi, Farshid
• Format: Journal Article
• Language: English
• Published: Oxford Royal Statistical Society 01.01.2015; Blackwell Publishing Ltd; John Wiley & Sons Ltd; Oxford University Press
• Subjects: air quality; Bands; Bandwidth choice; Bootstrap; Bootstrap resampling; Confidence; Confidence interval; Confidence intervals; Coverage accuracy; Density estimation; Double bootstrap; economics; Environmental science; Error; Error analysis; Error rates; Errors; Estimation; Estimation methods; Estimators; fat intake; Kernel methods; Mathematical models; Mathematical moments; Measurement error; Methodology; Non-parametric curve estimation; Non-parametric regression; Pointwise confidence band; Polynomials; Regression; Regression analysis; Setting; Simulation-extrapolation methods; Social sciences; Statistical analysis; Statistical variance; Statistics; Studies
• ISSN: 1369-7412; 1467-9868
• DOI: 10.1111/rssb.12067

Errors‐in‐variables regression is important in many areas of science and social science, e.g. in economics where it is often a feature of hedonic models, in environmental science where air quality indices are measured with error, in biology where the vegetative mass of plants is frequently obscured by mismeasurement and in nutrition where reported fat intake is typically subject to substantial error. To date, in non‐parametric contexts, the great majority of work has focused on methods for estimating the mean as a function, with relatively little attention being paid to techniques for empirical assessment of the accuracy of the estimator. We develop methodologies for constructing confidence bands. Our contributions include techniques for tuning parameter choice aimed at minimizing the coverage error of confidence bands.