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Total least squares and bootstrapping with applications in calibration. (English) Zbl 1440.62143
Summary: The solution to the errors-in-variables problem computed through total least squares is highly nonlinear. Because of this, many statistical procedures for constructing confidence intervals and testing hypotheses cannot be applied. One possible solution to this dilemma is bootstrapping. A nonparametric bootstrap technique could fail. Here, the proper nonparametric bootstrap procedure is provided and its correctness is proved. On the other hand, a residual bootstrap is not valid and suitable in this case. The results are illustrated through a simulation study. An application of this approach to calibration data is presented.

##### MSC:
 62G09 Nonparametric statistical resampling methods 62G05 Nonparametric estimation 62J05 Linear regression; mixed models 62P30 Applications of statistics in engineering and industry; control charts
##### Keywords:
total least squares; errors-in-variables; bootstrap; calibration
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##### References:
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