On lower and upper bounds of matrices

Gao, Peng

doi:10.1016/j.jmaa.2009.09.003

Cited by 2 publications

(2 citation statements)

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“…The difference between the true value on the left-hand side of the equation and the averaged value on the right-hand side is called the Jensen Gap. The size depends on the concavity of the response function, the difference between the two input rates, and the weighting of the points (Gao, Sitharam, and Roitberg 2019). Figure 5 presents an example of the Jensen Gap with a yield response function.…”

Section: 𝑓(𝜆mentioning

confidence: 99%

Impact of Machinery Misalignment on Economic Results through Jensen’s Inequality in On-Farm Precision Experiments

Edge¹,

Mieno²,

Bullock³

2023

Preprint

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This simulation study identifies the economic impact of treatment mixing on the estimated optimal nitrogen recommendations (EONR) from on-farm research and evaluates a data processing procedure to remove treatment mixing and improve the EONR. Treatment mixing is when the combine harvests from more than one treatment area at a time; this can be caused by a parallel shift in the ab-line, different application and harvest headings, or machinery with incompatible widths. Due to the concavity of the yield response curve to nitrogen, Jensen’s Inequality implies that treatment mixing will result in observations lying below the true yield response curve and may affect the resulting EONR. We simulate the effects of the three causes of treatment mixing, varying degrees of these causes, trial rates centered on different areas of the response curve, and different curvatures of the yield-response function on the estimated optimal nitrogen rates. We find that the impact of treatment mixing depends on all of these factors and their interactions. The trial rates have a large impact on the estimated yield response function because they shift the dataset along the yield response function. For example, if the rates are in a steep part of the response function, the estimated response function may overestimate the response to nitrogen. However, without knowledge of the true yield response function or EONR, a researcher cannot determine what trial rates are best for a given OFPE. In general, parallel shift or incompatible machinery have the largest impact on the estimation of optimal nitrogen, particularly a shift of half the combine width or a harvester that is smaller than the applicator. These scenarios result in average profit losses of as much as $37 per hectare. We find overestimation of the EONR is common with harvest misalignment, introducing environmental and economic impacts and reducing nitrogen use efficiency. These results highlight the importance of reducing treatment mixing in OFPE through communication with farmers, trial design, and improved data processing procedures. For example, when machinery is relatively small, designing trials that are twice the width of the combine ensures that each trial plot will have a pass of the combine without treatment mixing even if there is a parallel shift during harvesting. As OFPE are increasingly implemented, these are common problems researchers will be facing. This research shows that the implications of decisions around treatment mixing impact NUE and profitability of OFPE recommendations; thus, working on a common protocol around treatment mixing is important for the future of OFPE.

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Section: 𝑓(𝜆mentioning

confidence: 99%