Arbeitspapier
Optimal designs for estimating individual coefficients in polynomial regression: A functional approach
In this paper the optimal design problem for the estimation of the individual coefficients in a polynomial regression on an arbitrary interval [a, b] (- inf. < a < b < inf) is considered. Recently, Sahm (2000) demonstrated that the optimal design is one of four types depending on the symmetry parameter s = (a + b) / (a-b) and the specific coefficient which has to be estimated. In the same paper the optimal design was identified explicitly in three cases. It is the basic purpose of the present paper to study the remaining open fourth case. It will be proved that in this case the support points and weights are real analytic functions of the boundary points of the design space. This result is used to provide a Taylor expansion for the weights and support points as functions of the parameters a and b, which can easily be used for the numerical calculation of the optimal designs in all cases, which were not treated by Sahm (2000).
- Sprache
-
Englisch
- Erschienen in
-
Series: Technical Report ; No. 2001,01
- Thema
-
polynomial regression
c-optimal design
implicit function theorem
extremal polynomial
estimation of individual coefficients
- Ereignis
-
Geistige Schöpfung
- (wer)
-
Dette, Holger
Melas, Viatcheslav B.
Pepelyshev, Andrey
- Ereignis
-
Veröffentlichung
- (wer)
-
Universität Dortmund, Sonderforschungsbereich 475 - Komplexitätsreduktion in Multivariaten Datenstrukturen
- (wo)
-
Dortmund
- (wann)
-
2001
- Handle
- Letzte Aktualisierung
-
10.03.2025, 11:43 MEZ
Datenpartner
ZBW - Deutsche Zentralbibliothek für Wirtschaftswissenschaften - Leibniz-Informationszentrum Wirtschaft. Bei Fragen zum Objekt wenden Sie sich bitte an den Datenpartner.
Objekttyp
- Arbeitspapier
Beteiligte
- Dette, Holger
- Melas, Viatcheslav B.
- Pepelyshev, Andrey
- Universität Dortmund, Sonderforschungsbereich 475 - Komplexitätsreduktion in Multivariaten Datenstrukturen
Entstanden
- 2001
Ähnliche Objekte (12)
Efficient experimental designs for sigmoidal growth models
Optimal designs for dose finding experiments in toxicity studies
D-optimal designs for trigonometric regression models on a partial circle
Optimal designs for smoothing splines
Optimal designs for 3D shape analysis with spherical harmonic descriptors
Optimal designs for a class of nonlinear regression models
Optimal design in regression models with correlated errors
Maximin optimal designs for the compartmental model
Optimal designs for free knot least squares splines
Improving updating rules in multiplicativealgorithms for computing D-optimal designs
Locally E-optimal designs for exponential regression models
Some robust design strategies for percentile estimation in binary response models
Efficient experimental designs for sigmoidal growth models
Optimal designs for dose finding experiments in toxicity studies
D-optimal designs for trigonometric regression models on a partial circle
Optimal designs for smoothing splines
Optimal designs for 3D shape analysis with spherical harmonic descriptors
Optimal designs for a class of nonlinear regression models
Optimal design in regression models with correlated errors
Maximin optimal designs for the compartmental model
Optimal designs for free knot least squares splines
Improving updating rules in multiplicativealgorithms for computing D-optimal designs
Locally E-optimal designs for exponential regression models
Some robust design strategies for percentile estimation in binary response models
Efficient experimental designs for sigmoidal growth models
Optimal designs for dose finding experiments in toxicity studies
D-optimal designs for trigonometric regression models on a partial circle
Optimal designs for smoothing splines
Optimal designs for 3D shape analysis with spherical harmonic descriptors
Optimal designs for a class of nonlinear regression models
Optimal design in regression models with correlated errors
Maximin optimal designs for the compartmental model
Optimal designs for free knot least squares splines
Improving updating rules in multiplicativealgorithms for computing D-optimal designs
Locally E-optimal designs for exponential regression models