Nonparametric regression as an example of model choice

Nonparametric regression can be considered as a problem of model choice. In this paper we present the results of a simulation study in which several nonparametric regression techniques including wavelets and kernel methods are compared with respect to their behaviour on different test beds. We also include the taut-string method whose aim is not to minimize the distance of an estimator to some ?true? generating function f but to provide a simple adequate approximation to the data. Test beds are situations where a ?true? generating f exists and in this situation it is possible to compare the estimates of f with f itself. The measures of performance we use are the L2 and the L1 norms and the ability to identify peaks. --

The benchden package

This article describes the benchden package which implements a set of 28 example densities for nonparametric density estimation in R. In addition to the usual functions that evaluate the density, distribution and quantile functions or generate random variates, a function designed to be specifically useful for larger simulation studies has been added. After describing the set of densities and the usage of the package, a small toy example of a simulation study conducted using the benchden package is given

Constructing a regular histogram : a comparison of methods

Even for a well-trained statistician the construction of a histogram for a given real-valued set is a sifficult problem. It is even more difficult to construct a fully automatic procedure which specifies the number and widths of the binss in a satisfactory manner for a wide range of data sets. In this paper we compare several histogram construction methods by means of a simulation study. The study includes plug-in methods, cross-validation, penalized maximum likehood and the taut string procedure. Their performance on different test beds is measured by the Hellinger distance and the ability to identify the modes of the underlying density. --regular histogramm,model selection,penalized likehood,taut-string

Extremstellenverlust als Gütekriterium in der nichtparametrischen Regression

In dieser Arbeit wird ein neues Gütekriterium für den Vergleich verschiedener nichtparametrischer Regressionsmethoden erarbeitet. Die nichtparametrische Regression befasst sich damit, aus gegebenen Daten eine Signalfunktion zu schätzen. Zur Gegenüberstellung verschiedener Regressionsverfahren werden häufig Simulationsstudien durchgeführt, in denen die Verfahren auf Daten angewandt werden, deren zugrundeliegende Signalfunktion bekannt ist. Der Vergleich mehrerer Schätzfunktionen basiert auf Gütekriterien, wobei zumeist Lp-Normen verwendet werden. Dabei besteht eine Diskrepanz zwischen dem, was diese Normen messen, und der visuellen Beurteilung durch einen Betrachter, da die Normen nur den vertikalen Abstand von Signal- und Schätzfunktion verwenden. Ein Betrachter kann beispielsweise falsch geschätzte Extremwerte visuell sofort erfassen und zieht sie automatisch zur Bewertung der Schätzfunktion heran. Insbesondere für Anwendungen, bei denen das korrekte Identifizieren von Extremwerten von hoher Bedeutung ist, führen klassische Gütekriterien wie die Lp -Normen zu Fehleinschätzungen bezüglich der Eignung von Regressionsverfahren. In der vorliegenden Arbeit wird daher ein gänzlich neues Gütemaß für die Beurteilung der Anpassung an Signalfunktionen vorgeschlagen. Der neue Extremstellenverlust bewertet die korrekte Identifizierung von Extrema. Für eine Schätzfunktion wird dafür zunächst überprüft, ob ihre Extremstellen mit denen der Signalfunktion übereinstimmen. Daraufhin wird das Fehlverhalten zu viel und zu wenig geschätzter Extremstellen in einem normierten Verlust zusammengefasst. Damit formalisiert das neue Kriterium die visuelle Beurteilung durch einen Betrachter und ist geeignet, die Güte einer Regressionsmethode bezüglich ihrer Extremwerte in einem Verlustwert zu erfassen

Nr. 14/2011The benchden Package: Benchmark Densities for Nonparametric Density Estimation

The benchden package: Benchmark densities for nonparametric density estimatio

Cracking percent problems in different formats: The role of texts and visual models for students with low and high language proficiency

International audienceStudents with low academic language proficiency are often considered to meet specific comprehension challenges with word problems. But how do conceptual and reading challenges interfere in these situations? We approach this question by investigating how performance depends on the problem format for different problem types. A test with N=250 students investigates cracking percent problems in pure, text, and visual format. The results show that text formats are most difficult for elementary problem types, whereas (context t can enhance the accessibility for more complex problem types. Item difficulties differ similarly for students with high and low language proficiency, hence reading challenges seem as crucial as conceptual challenges. A deeper analysis shows specific linguistic challenges with the expressions reduced to and reduced by

Cracking percent problems in different formats: The role of texts and visual models for students with low and high language proficiency

International audienceStudents with low academic language proficiency are often considered to meet specific comprehension challenges with word problems. But how do conceptual and reading challenges interfere in these situations? We approach this question by investigating how performance depends on the problem format for different problem types. A test with N=250 students investigates cracking percent problems in pure, text, and visual format. The results show that text formats are most difficult for elementary problem types, whereas (context t can enhance the accessibility for more complex problem types. Item difficulties differ similarly for students with high and low language proficiency, hence reading challenges seem as crucial as conceptual challenges. A deeper analysis shows specific linguistic challenges with the expressions reduced to and reduced by

Which factors coincide with mathematical learning gains in bilingual classrooms?

Although bilingual mathematical learning opportunities have often been requested for multilingual students, little quantitative evidence has been provided that activating two languages has measurable effects on learning gains. This study uses data from a bilingual teaching intervention to investigate which factors coincide most with the mathematical learning gains in conceptual understanding of fractions. Students’ individual and family characteristics have been assessed and participation and language use have been coded in ~95h videotaped teaching-learning processes. A regression analysis shows that students’ learning gains can best be explained by students’ German language proficiency and their use of Turkish and mixed mode, while talking time did not coincide with learning gains. Thus, the connection of languages seems to be even more important for mathematical learning gains than the isolated use of home languages or active participation

Which factors coincide with mathematical learning gains in bilingual classrooms?

Although bilingual mathematical learning opportunities have often been requested for multilingual students, little quantitative evidence has been provided that activating two languages has measurable effects on learning gains. This study uses data from a bilingual teaching intervention to investigate which factors coincide most with the mathematical learning gains in conceptual understanding of fractions. Students’ individual and family characteristics have been assessed and participation and language use have been coded in ~95h videotaped teaching-learning processes. A regression analysis shows that students’ learning gains can best be explained by students’ German language proficiency and their use of Turkish and mixed mode, while talking time did not coincide with learning gains. Thus, the connection of languages seems to be even more important for mathematical learning gains than the isolated use of home languages or active participation