Details
| Original language | English |
|---|---|
| Pages (from-to) | 286-306 |
| Number of pages | 21 |
| Journal | International Journal of Reliability and Safety |
| Volume | 3 |
| Issue number | 1-3 |
| Publication status | E-pub ahead of print - 27 Jun 2009 |
Abstract
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).
Keywords
- Fuzzy, Hypothesis testing, Imprecision, Linear models, Probability, Type I error, Type II error
ASJC Scopus subject areas
- Engineering(all)
- Safety, Risk, Reliability and Quality
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In: International Journal of Reliability and Safety, Vol. 3, No. 1-3, 27.06.2009, p. 286-306.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - The probability of type I and type II errors in imprecise hypothesis testing with an application to geodetic deformation analysis
AU - Neumann, Ingo
AU - Kutterer, Hansjörg
PY - 2009/6/27
Y1 - 2009/6/27
N2 - 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).
AB - 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).
KW - Fuzzy
KW - Hypothesis testing
KW - Imprecision
KW - Linear models
KW - Probability
KW - Type I error
KW - Type II error
UR - http://www.scopus.com/inward/record.url?scp=78651591317&partnerID=8YFLogxK
M3 - Article
AN - SCOPUS:78651591317
VL - 3
SP - 286
EP - 306
JO - International Journal of Reliability and Safety
JF - International Journal of Reliability and Safety
SN - 1479-389X
IS - 1-3
ER -