The probability of type I and type II errors in imprecise hypothesis testing with an application to geodetic deformation analysis

In many engineering disciplines the interesting model parameters are estimated from a large number of heterogeneous and redundant observations by a least-squares adjustment. The significance of the model parameters, outlier detection and the model selection itself are checked within statistical hypothesis tests. The acceptance and the rejection of the hypothesis are strongly related with two types of errors. A type I error occurs if the null hypothesis is rejected, although it is true. A type II error occurs if the null hypothesis is accepted, although it is false. This paper proposes a general procedure to hypothesis testing in linear parameter estimation, if the uncertainty is considered by random variability and interval/fuzzy errors. The study focuses on the probability of type I and type II errors. The applied procedure is outlined in detail showing both theory and numerical examples for the parameterisation of a geodetic monitoring network (deformation analysis).