Asymptotic criteria for designs in nonlinear regression with model errors

Andrej Pázman; Luc Pronzato

Mathematica Slovaca (2006)

  • Volume: 56, Issue: 5, page 543-553
  • ISSN: 0232-0525

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Pázman, Andrej, and Pronzato, Luc. "Asymptotic criteria for designs in nonlinear regression with model errors." Mathematica Slovaca 56.5 (2006): 543-553. <http://eudml.org/doc/31690>.

@article{Pázman2006,
author = {Pázman, Andrej, Pronzato, Luc},
journal = {Mathematica Slovaca},
keywords = {nonlinear regression; least squares; optimum design; asymptotic normality; measures of nonlinearity; information matrix},
language = {eng},
number = {5},
pages = {543-553},
publisher = {Mathematical Institute of the Slovak Academy of Sciences},
title = {Asymptotic criteria for designs in nonlinear regression with model errors},
url = {http://eudml.org/doc/31690},
volume = {56},
year = {2006},
}

TY - JOUR
AU - Pázman, Andrej
AU - Pronzato, Luc
TI - Asymptotic criteria for designs in nonlinear regression with model errors
JO - Mathematica Slovaca
PY - 2006
PB - Mathematical Institute of the Slovak Academy of Sciences
VL - 56
IS - 5
SP - 543
EP - 553
LA - eng
KW - nonlinear regression; least squares; optimum design; asymptotic normality; measures of nonlinearity; information matrix
UR - http://eudml.org/doc/31690
ER -

References

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  1. BATES D. M.-WATTS D. G., Nonlinear Regression Analysis and its Applications, Wileу, New York, 1988. (1988) Zbl0728.62062MR1060528
  2. GALLANT A. R., Nonlinear Statistical Models, Wileу, New York, 1987. (1987) Zbl0611.62071MR0921029
  3. HARVILLE D. A., Matrix Algebra from a Statistician's Perspective, Springer, New York, 1997. (1997) Zbl0881.15001MR1467237
  4. IVANOV A. V., Asymptotic Theory of Nonlinear Regression, Kluwer, Dordrecht, 1997. (1997) Zbl0874.62070MR1472234
  5. JENNRICH R. L., Asymptotic properties of nonlinear least squares estimation., Ann. Math. Statist. 40 (1969), 633-643. (1969) MR0238419
  6. KIEFER J., Optimum design for fitting biased multivariate surfaces, In: Multivariate Analуsis (P. R. Krishnaian, ed.), North Holland, Amsterdam, 1973, pp. 287-297. (1973) MR0365936
  7. PÁZMAN A., Nonlinear Statistical Models, Kluwer, Dordrecht, 1993. (1993) Zbl0808.62058MR1254661
  8. PÁZMAN A.-PRONZATO L., On the irregular behavior of LS estimators for asymptotically singular designs, Lab. IЗS, CNRS Sophia Antipolis. Rapport de recherche ISRN IЗS/RR-2005-12-FR, Juin 2005 [Statist. & Probab. Lett. 76 (2006), 1089-1096]. Zbl1090.62076MR2269278
  9. PESOTCHINSKI L., Optimal robust designs: linear regression in R k , Ann. Statist. 10 (1982), 511-525. (1982) MR0653526
  10. PUKELSHEIM F., Optimal Experimental Design, Wileу, New York, 1993. (1993) MR1211416
  11. WELCH W. J., A mean squared error criterion for the design of experiments, Biometrika 70 (1983), 205-213. (1983) Zbl0517.62066MR0742990

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