Properly recorded estimate and confidence regions obtained by an approximate covariance operator in a special nonlinear model

Gejza Wimmer

Applications of Mathematics (1995)

  • Volume: 40, Issue: 6, page 411-431
  • ISSN: 0862-7940

Abstract

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The properly recorded standard deviation of the estimator and the properly recorded estimate are introduced. Bounds for the locally best linear unbiased estimator and estimate and also confidence regions for a linearly unbiasedly estimable linear functional of unknown parameters of the mean value are obtained in a special structure of nonlinear regression model. A sufficient condition for obtaining the properly recorded estimate in this model is also given.

How to cite

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Wimmer, Gejza. "Properly recorded estimate and confidence regions obtained by an approximate covariance operator in a special nonlinear model." Applications of Mathematics 40.6 (1995): 411-431. <http://eudml.org/doc/32930>.

@article{Wimmer1995,
abstract = {The properly recorded standard deviation of the estimator and the properly recorded estimate are introduced. Bounds for the locally best linear unbiased estimator and estimate and also confidence regions for a linearly unbiasedly estimable linear functional of unknown parameters of the mean value are obtained in a special structure of nonlinear regression model. A sufficient condition for obtaining the properly recorded estimate in this model is also given.},
author = {Wimmer, Gejza},
journal = {Applications of Mathematics},
keywords = {properly recorded estimate; nonlinear regression; variances depending on the mean value parameters; confidence regions; bounds for the estimate; bounds; variance depending on mean value parameters; properly recorded standard deviation; properly recorded estimate; locally best linear unbiased estimator; confidence regions; linearly unbiasedly estimable linear functional; mean value},
language = {eng},
number = {6},
pages = {411-431},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Properly recorded estimate and confidence regions obtained by an approximate covariance operator in a special nonlinear model},
url = {http://eudml.org/doc/32930},
volume = {40},
year = {1995},
}

TY - JOUR
AU - Wimmer, Gejza
TI - Properly recorded estimate and confidence regions obtained by an approximate covariance operator in a special nonlinear model
JO - Applications of Mathematics
PY - 1995
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 40
IS - 6
SP - 411
EP - 431
AB - The properly recorded standard deviation of the estimator and the properly recorded estimate are introduced. Bounds for the locally best linear unbiased estimator and estimate and also confidence regions for a linearly unbiasedly estimable linear functional of unknown parameters of the mean value are obtained in a special structure of nonlinear regression model. A sufficient condition for obtaining the properly recorded estimate in this model is also given.
LA - eng
KW - properly recorded estimate; nonlinear regression; variances depending on the mean value parameters; confidence regions; bounds for the estimate; bounds; variance depending on mean value parameters; properly recorded standard deviation; properly recorded estimate; locally best linear unbiased estimator; confidence regions; linearly unbiasedly estimable linear functional; mean value
UR - http://eudml.org/doc/32930
ER -

References

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  1. Projection with the wrong inner product and its application to regression with correlated errors and linear filtering of time series, The Annals of Math. Statistics 42 (1971), 616-624. (1971) Zbl0234.62026MR0286236
  2. Handbuch Messtechnik und Qualitätsicherung, VEB Verlag Technik, Berlin, 1986. (1986) 
  3. Statistische Methoden der Modellbildung III, Akademie Verlag, Berlin, 1984. (1984) Zbl0556.62051MR0755875
  4. Foundations of Estimation Theory, Elsevier, Amsterdam, 1988. (1988) MR0995671
  5. Jordan/Eggert/Kneissl Handbuch der Vermessungskunde, Band VI, Stuttgart, 1971. (1971) 

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