A confidence set for that x-coordinate where a quadratic regression model has a given gradient

Statistical Papers

Volumn 50, Issue 3, 2009, Pages 649-660

  Bachmaier, Martin ^a  

^a TECHNICAL UNIVERSITY OF MUNICH   (Germany)

Author keywords

Confidence interval; Confidence set; Gradient; Optimization problem; Parabola; Quadratic model; Vertex

Indexed keywords

EID: 67349280495     PISSN: 09325026     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00362-007-0104-1     Document Type: Article

References (14)

1. Bachmaier M (2005) Fortran Programs: 1. Confidence set for the economically optimum nitrogen fertilization in the quadratic model: VINO.EXE. 2. Confidence set for that x-coordinate where the quadratic regression model has a given gradient (incl. special case: confidence set for the x-coordinate of the parabola's vertex): CIGIGRAD.EXE and CIVERTEX.EXE. To be downloaded from http://www.tec.wzw.tum.de/pflanztech/englisch/personen/bachmaier/bachmaier.html
2. DA Boyd LTK Yuen P Needham 1976 Nitrogen requirement of cereals J Agric Sci 87 149 162
3. DG Bullock DS Bullock 1986 Quadratic and quadratic-plus-plateau models for predicting optimal nitrogen rate of corn: a comparison Agron J 86 191 195
4. Casella G and Berger RL (2002). Statistical inference. Duxbury Press, Belmont
5. ME Cerrato AM Blackmer 1990 Comparison of models for describing corn yield response to nitrogen fertilizer Agron J 82 138 143
6. Colwell JD (1994). Estimating fertilizer requirements: a quantitative approach. CAB International, Oxfordshire
7. Dabbert S, Kilian B (2002) Ökonomie. In: Werner A, Jarfe A (eds) Precision Agriculture-Herausforderung an integrative Forschung, Entwicklung und Anwendung in der Praxis. KTBL-Sonderveröffentlichung 38:423-446
8. EC Fieller 1954 Some problems in interval estimation J R Stat Soc Ser B 16 175 185
9. TM Hurley GL Malzer B Kilian 2004 Estimating site-specific nitrogen crop response functions: a conceptual framework and geostatistical model Agron J 96 1331 1343 (Pubitemid 39252097)
10. D Koziol W Zielinski 2003 Comparison of confidence intervals for maximum of a quadratic regression function Listy Biometryczne (Biom Lett) 40 57 64
11. RM Lark HC Wheeler 2003 A method to investigate within-field variation of the response of combinable crops to an input Agron J 95 1093 1104 (Pubitemid 37216201)
12. M Le Bail M-H Jeuffroy C Bouchard A Barbottin 2005 Is it possible to forecast the grain quality and yield of different varieties of winter wheat from Minolta SPAD meter measurements? Eur J Agron 23 379 391 (Pubitemid 41565588)
13. Mittelhammer RC, Judge GG and Miller DJ (2000). Econometric foundations. Cambridge University Press, Cambridge
14. P Wagner 1999 Produktionsfunktionen und Precision Farming (response functions in the context of precision farming). Zukunftsorientierte Betriebswirtschaft und Informationstechnologien in der Agrarwirtschaft Giessener Schriften zur Agrar- und Ernährungswirtschaft 29 39 66