Papers by Martin Bachmaier
Aufgabensammlung mit Lösungen zur Mathematik für Nichtmathematiker, 2006
Aufgabensammlung mit Lösungen zur Mathematik für Nichtmathematiker, 2006
Aufgabensammlung mit Lösungen zur Mathematik für Nichtmathematiker, 2006
The objective of this article is to address the frequently found academic opinion that in order t... more The objective of this article is to address the frequently found academic opinion that in order to calculate the population variance, the sum of the squared deviations from the mean should be divided by the non-reduced number of summands, and not, as is the case for the sample variance, by one less. In reality, the question regarding the subtraction of one has nothing to do with whether it concerns a population or a sample; the decisive factor is whether the sum of squares refers to all measurement values or to characteristic values that are equally probable (or frequent). In the latter case, the full number is the divisor. However, if the sum of squares contains all measurement values of a sample or a population, one must be deducted from the overall number before it can be considered suitable as a divisor. Nevertheless, and precisely because of this subtraction, the variance becomes an average spread in the sense that it is not subject to a trend with regard to the number of data ...
Anhand der Abdrifteckwerte fur Einfachanwendungen beim Ackerbau der BBA wird die Verteilung des P... more Anhand der Abdrifteckwerte fur Einfachanwendungen beim Ackerbau der BBA wird die Verteilung des Pflanzenschutzmittels aus der Flachstrahlduse einer Spritze durch eine abgeschnittene Cauchy-Verteilung modelliert. Diese entspricht einem gleichverteilten Spritzen auf einem Kreissektor bis zu 90° in Hauptwindrichtung und bis zu einem kleineren Winkel j gegen die Hauptwindrichtung. Es wird eine Formel fur die auf eine bestimmte Nichtzielflache in Hauptwindrichtung insgesamt abgedriftete Menge an Pflanzenschutzmitteln (PSM) angegeben.
The objective of this article is to address the frequently found academic opinion that in order t... more The objective of this article is to address the frequently found academic opinion that in order to calculate the population variance, the sum of the squared deviations from the mean should be divided by the non-reduced number of summands, and not, as is the case for the sample variance, by one less. In reality, the question regarding the subtraction of one has nothing to do with whether it concerns a population or a sample; the decisive factor is whether the sum of squares refers to all measurement values or to characteristic values that are equally probable (or frequent). In the latter case, the full number is the divisor. However, if the sum of squares contains all measurement values of a sample or a population, one must be deducted from the overall number before it can be considered suitable as a divisor. Nevertheless, and precisely because of this subtraction, the variance becomes an average spread in the sense that it is not subject to a trend with regard to the number of data ...
Durch die Vernetzung elektronischer Steuerungssysteme werden neue Moglichkeiten fur das tierindiv... more Durch die Vernetzung elektronischer Steuerungssysteme werden neue Moglichkeiten fur das tierindividuelle Kalbermanagement eroffnet. Die verschiedenen Systeme werden dabei als automatisierte Systeme oder als Vollautomaten aufgebaut, um den Arbeitsaufwand zu reduzieren. In dieser Veroffentlichung wird der Aufbau des zu Grunde liegenden Versuchs beschrieben und erste Ergebnisse in Verbindung mit einer statistischen Auswertung der Futterungsdaten dargestellt. Dabei werden Aufnahmemengen von Wasser und Trockensubstanz der Kalber in Abhangigkeit des Alters aufgezeigt. Die Ergebnisse bestatigen die Notwendigkeit einer tierindividuellen Anpassung des Trankregimes. Alle bekannten Au-toren beziehen sich diesbezuglich entweder auf die Trinkwasser-, Kraftfutter-, Grundfutteraufnahme oder das Tiergewicht, aber nicht auf eine Kombination dieser Daten. Der Einsatz einer automatischen, vernetzten Futterungstechnik hat in vielerlei Hinsicht okonomische Vorteile und bietet eine umfassende Entscheidun...
Aufgabensammlung mit Lösungen zur Mathematik für Nichtmathematiker, 2006
Aufgabensammlung mit Lösungen zur Mathematik für Nichtmathematiker
Positioning, 2010
The yield map is generated by fitting the yield surface shape of yield monitor data mainly using ... more The yield map is generated by fitting the yield surface shape of yield monitor data mainly using paraboloid cones on floating neighborhoods. Each yield map value is determined by the fit of such a cone on an elliptical neighborhood that is wider across the harvest tracks than it is along them. The coefficients of regression for modeling the paraboloid cones and the scale parameter are estimated using robust weighted M-estimators where the weights decrease quadratically from 1 in the middle to zero at the border of the selected neighborhood. The robust way of estimating the model parameters supersedes a procedure for detecting outliers. For a given neighborhood shape, this yield mapping method is implemented by the Fortran program paraboloidmapping.exe, which can be downloaded from the web. The size of the selected neighborhood is considered appropriate if the variance of the yield map values equals the variance of the true yields, which is the difference between the variance of the raw yield data and the error variance of the yield monitor. It is estimated using a robust variogram on data that have not had the trend removed.
The purpose of this paper is to estimate the variance of the yields of a field by means of a vari... more The purpose of this paper is to estimate the variance of the yields of a field by means of a variogram. It will turn out that we can only estimate the variance of yields smoothed with respect to positioning errors as we do not know the true position of the measuring value exactly. This kind of field variance can serve mainly for judging data correction methods whether they smooth too much or too little. How could we know if corrected data are too homogeneous or too heterogeneous if we had no measure for the heterogeneity of a field which is independent of this method? Such a measure is urgently necessary because the actual position error smoothed field variance is often much smaller than the measuring values let us guess. The large dispersion of the measured yield values is usually predominantly based on the great error variance of the measuring system (the nugget) or on positioning errors that are lesser caused by the inaccuracy of the GPS system than by inaccurate lags between har...
This paper deals with yield maps derived from yield monitor data of a combine harvester. Every va... more This paper deals with yield maps derived from yield monitor data of a combine harvester. Every value of the yield map is determined by robust fitting of a paraboloid surface over a spatial neighborhood around the point to be mapped, so that the influence of outliers is bounded or canceled completely. The neighborhood used looks like the top view of the shape of the wings of a butterfly gliding along the harvest tracks. To determine the optimal size and shape of the neighborhood, an experiment was conducted with yield data measured by a plot combine (called as true values) as well as yield monitor data from a commercial combine with a wider head, which then harvested the same stretch behind the plot combine. The commercial combine was equipped with two monitors. The yield maps are considered to have been optimized if the mean squared deviations (mean squared error) between the true and mapped values has been minimized. A large neighborhood proved necessary for both yield monitors, wi...
Every value of the yield map is determined by robust fitting of a paraboloid surface over a spati... more Every value of the yield map is determined by robust fitting of a paraboloid surface over a spatial neighborhood of yield monitor data around the point to be mapped, so that the influence of outliers is bounded or canceled completely. The neighborhood used looks like the top view of the shape of the wings of a butterfly gliding along the harvest tracks. To determine the optimal size and shape of the neighborhood, an experiment was conducted with yield data measured by a plot combine (called as true values) as well as yield monitor data from a commercial combine with a wider head, which then harvested the same stretch behind the plot combine. The commercial combine was equipped with two monitors. The yield maps are considered to have been optimized if the mean squared deviations (mean squared error) between the true and mapped values has been minimized. A large neighborhood proved necessary for both yield monitors, with the result that the best yield maps obtained appear to be very s...
Statistical Papers, 1995
This paper describes how to compute robust confidence intervals for differences of the effects us... more This paper describes how to compute robust confidence intervals for differences of the effects using the likelihood ratio testF M in the two-way analysis of variance. The probability for the α-error and the average length of the confidence intervals withF m and the quadratic formQ M are investigated and compared with the classical confidence intervals fort-distributed and lognormal errors. We also give a warning of building confidence intervals withF M andQ M in the presence of heterogeneous scale parameters, because these tests which do not regard heteroscedasticity are then much too liberal.
Statistical Papers, 2007
An exact confidence set for that x-coordinate where a quadratic regression model has a given grad... more An exact confidence set for that x-coordinate where a quadratic regression model has a given gradient is derived. The limits of the confidence set are given by mathematical formulae. They are implemented in Fortran programs that can be downloaded from the web. The confidence set need not be an interval. Its increase and its changing shape for increasing confidence level is extensively described and visualized in a figure that relates to data from nitrogen-rate trials in Germany. The wheat yields in this example are modeled as quadratic functions of the nitrogen input in order to determine a confidence set for the economically optimum nitrogen fertilization. The disadvantage that the confidence set does not distinguish between concave and convex parabolae, between profit maxima and minima, is also discussed.
Statistical Papers, 2008
In this article, an exact test and a confidence set for the difference of the x-coordinates of th... more In this article, an exact test and a confidence set for the difference of the x-coordinates of the vertices of quadratic regression models is derived. It is assumed that the quadratic coefficients of both parabolae are equal, so the mentioned difference can equally be related to those x-coordinates where the parabolae have definite given gradient. The limits of the confidence set are given by mathematical formulae. They are implemented in Fortran programs that can be downloaded from the web. The confidence set need not be an interval. This is shown by an example based on nitrogen-rate trials in Germany, where the wheat yields are modeled as quadratic functions of the nitrogen input.
Statistical Papers, 2000
In this paper an alternative measure for the excess, called standard arch a&, is introduced. It i... more In this paper an alternative measure for the excess, called standard arch a&, is introduced. It is only an affine transformation of the classical kurtosis, but has many advantages. It can be defined as the double relative asymptotic variance of the standard deviation and can be generalized as the double relative asymptotic variance of any other scale estimator. The inequalities between skewness and kurtosis given in TEUSCHER and GUIARD (1995) are transformed to the corresponding inequalities between skewness and standard arch.
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Papers by Martin Bachmaier