Details
| Original language | English |
|---|---|
| Title of host publication | VII Hotine-Marussi Symposium on Mathematical Geodesy - Proceedings of the Symposium |
| Publisher | Springer Verlag |
| Pages | 75-80 |
| Number of pages | 6 |
| ISBN (Electronic) | 978-3-642-22078-4 |
| ISBN (Print) | 9783642220777 |
| Publication status | Published - 2012 |
| Externally published | Yes |
| Event | VII Hotine-Marussi Symposium on Mathematical Geodesy - Rome, Italy Duration: 6 Jun 2009 → 10 Jun 2009 Conference number: 7 |
Publication series
| Name | International Association of Geodesy Symposia |
|---|---|
| Volume | 137 |
| ISSN (Print) | 0939-9585 |
Abstract
In this study hypothesis testing is treated, when neither the probability density function (pdf) of the test statistic under the null hypothesis nor the pdf of the test statistic under the alternative hypothesis are known. First, the classical procedure in case of random variability is reviewed. Then, the testing procedure is extended to the case when the uncertainty of the measurements comprises both random and systematic errors. Both types of uncertainty are treated in a comprehensive way using fuzzy-random variables (FRVs) which represent a combination of probability and fuzzy theory. The classical case of random errors (absence of systematic errors) is a special case of FRVs. The underlying theory of the procedure is outlined in particular. The approach allows the consideration of fuzzy regions of acceptance and rejection. The final (optimal) test decision is based on the utility theory which selects the test decision with the largest expected utility as the most beneficial one. An example illustrates the theoretical concept.
Keywords
- Decision making, Fuzzy data analysis, Hypothesis testing, Imprecise data, Regulatory thresholds, Utility theory
ASJC Scopus subject areas
- Earth and Planetary Sciences(all)
- Computers in Earth Sciences
- Earth and Planetary Sciences(all)
- Geophysics
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VII Hotine-Marussi Symposium on Mathematical Geodesy - Proceedings of the Symposium. Springer Verlag, 2012. p. 75-80 (International Association of Geodesy Symposia; Vol. 137).
Research output: Chapter in book/report/conference proceeding › Conference contribution › Research › peer review
}
TY - GEN
T1 - Optimal Hypothesis Testing in Case of Regulatory Thresholds
AU - Neumann, I.
AU - Kutterer, H.
N1 - Conference code: 7
PY - 2012
Y1 - 2012
N2 - In this study hypothesis testing is treated, when neither the probability density function (pdf) of the test statistic under the null hypothesis nor the pdf of the test statistic under the alternative hypothesis are known. First, the classical procedure in case of random variability is reviewed. Then, the testing procedure is extended to the case when the uncertainty of the measurements comprises both random and systematic errors. Both types of uncertainty are treated in a comprehensive way using fuzzy-random variables (FRVs) which represent a combination of probability and fuzzy theory. The classical case of random errors (absence of systematic errors) is a special case of FRVs. The underlying theory of the procedure is outlined in particular. The approach allows the consideration of fuzzy regions of acceptance and rejection. The final (optimal) test decision is based on the utility theory which selects the test decision with the largest expected utility as the most beneficial one. An example illustrates the theoretical concept.
AB - In this study hypothesis testing is treated, when neither the probability density function (pdf) of the test statistic under the null hypothesis nor the pdf of the test statistic under the alternative hypothesis are known. First, the classical procedure in case of random variability is reviewed. Then, the testing procedure is extended to the case when the uncertainty of the measurements comprises both random and systematic errors. Both types of uncertainty are treated in a comprehensive way using fuzzy-random variables (FRVs) which represent a combination of probability and fuzzy theory. The classical case of random errors (absence of systematic errors) is a special case of FRVs. The underlying theory of the procedure is outlined in particular. The approach allows the consideration of fuzzy regions of acceptance and rejection. The final (optimal) test decision is based on the utility theory which selects the test decision with the largest expected utility as the most beneficial one. An example illustrates the theoretical concept.
KW - Decision making
KW - Fuzzy data analysis
KW - Hypothesis testing
KW - Imprecise data
KW - Regulatory thresholds
KW - Utility theory
UR - http://www.scopus.com/inward/record.url?scp=84884371577&partnerID=8YFLogxK
U2 - 10.1007/978-3-642-22078-4_11
DO - 10.1007/978-3-642-22078-4_11
M3 - Conference contribution
AN - SCOPUS:84884371577
SN - 9783642220777
T3 - International Association of Geodesy Symposia
SP - 75
EP - 80
BT - VII Hotine-Marussi Symposium on Mathematical Geodesy - Proceedings of the Symposium
PB - Springer Verlag
T2 - VII Hotine-Marussi Symposium on Mathematical Geodesy
Y2 - 6 June 2009 through 10 June 2009
ER -