Linearization regions for confidence ellipsoids

Lubomír Kubáček; Eva Tesaříková

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica (2008)

  • Volume: 47, Issue: 1, page 101-113
  • ISSN: 0231-9721

Abstract

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If an observation vector in a nonlinear regression model is normally distributed, then an algorithm for a determination of the exact ( 1 - α ) -confidence region for the parameter of the mean value of the observation vector is well known. However its numerical realization is tedious and therefore it is of some interest to find some condition which enables us to construct this region in a simpler way.

How to cite

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Kubáček, Lubomír, and Tesaříková, Eva. "Linearization regions for confidence ellipsoids." Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 47.1 (2008): 101-113. <http://eudml.org/doc/32469>.

@article{Kubáček2008,
abstract = {If an observation vector in a nonlinear regression model is normally distributed, then an algorithm for a determination of the exact $(1-\alpha )$-confidence region for the parameter of the mean value of the observation vector is well known. However its numerical realization is tedious and therefore it is of some interest to find some condition which enables us to construct this region in a simpler way.},
author = {Kubáček, Lubomír, Tesaříková, Eva},
journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
keywords = {confidence ellipsoid; nonlinear regression model; linearization region; nonlinear regression model; linearization region},
language = {eng},
number = {1},
pages = {101-113},
publisher = {Palacký University Olomouc},
title = {Linearization regions for confidence ellipsoids},
url = {http://eudml.org/doc/32469},
volume = {47},
year = {2008},
}

TY - JOUR
AU - Kubáček, Lubomír
AU - Tesaříková, Eva
TI - Linearization regions for confidence ellipsoids
JO - Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
PY - 2008
PB - Palacký University Olomouc
VL - 47
IS - 1
SP - 101
EP - 113
AB - If an observation vector in a nonlinear regression model is normally distributed, then an algorithm for a determination of the exact $(1-\alpha )$-confidence region for the parameter of the mean value of the observation vector is well known. However its numerical realization is tedious and therefore it is of some interest to find some condition which enables us to construct this region in a simpler way.
LA - eng
KW - confidence ellipsoid; nonlinear regression model; linearization region; nonlinear regression model; linearization region
UR - http://eudml.org/doc/32469
ER -

References

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  1. Bates D. M., Watts D. G., Relative curvature measures of nonlinearity, J. Roy. Stat. Soc. B 42 (1980), 1–25. (1980) Zbl0455.62028MR0567196
  2. Kubáček L., Kubáčková L., Volaufová J.: Statistical Models with Linear Structures., Veda (Publishing House of Slovak Academy of Science), Bratislava, , 1995. (1995) 
  3. Kubáček L., On a linearization of regression models, Applications of Mathematics 40 (1995), 61–78. (1995) MR1305650
  4. Kubáček L., Kubáčková L., Regression models with a weak nonlinearity, Technical report Nr. 1998.1, Universität Stuttgart, 1998, 1–67. (1998) 
  5. Kubáček L., Kubáčková L.: Statistics, Metrology., Vyd. Univ. Palackého, Olomouc, , 2000 (in Czech). 
  6. Kubáček L., Tesaříková E., Confidence regions in nonlinear models with constraints, Acta Univ. Palacki. Olomuc., Fac. rer. nat., Math. 42, 2003, 407–426. Zbl1046.62065MR2056021
  7. Kubáčková L.: Foundations of Experimental Data Analysis., CRC-Press, Boca Raton-Ann Arbor–London–Tokyo, , 1992. (1992) MR1244322
  8. Pázman A.: Nonlinear Statistical Models., Kluwer Academic Publisher, Dordrecht–Boston–London and Ister Science Press, Bratislava, , 1993. (1993) MR1254661
  9. Tesaříková E., Kubáček L., How to deal with regression models with a weak nonlinearity, Discuss. Math., Probab. Stat. 21, 2001, 21–48. MR1868926
  10. Tesaříková E., Kubáček L., Estimators of dispersion in models with constraints (demoprogram), Dept. Algebra and Geometry, Fac. Sci., Palacký Univ., Olomouc, 2003. 
  11. Tesaříková E., Kubáček L., Linearization regions for confidence ellipsoids (demoprogram), Department of Algebra and Geometry, Faculty of Dept. Algebra and Geometry, Fac. Sci., Palacký Univ., Olomouc, 2007. MR2482720

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