Zdeněk Hlávka

You Like It, You Learn It: Affectivity and Learning in Competitive Social Role Play Gaming.

Despite the alleged ability of digital game-based learning (DGBL) to foster positive affect and in turn improve learning, the link between affectivity and learning has not been sufficiently investigated in this field. Regarding learning from team-based games with competitive elements, even less is known about the relationship between competitiveness (as a dispositional trait) and induced positive affect. In this media comparison study with between-subject design, participants (N = 325; high school and college students) learned about the EU’s policy agenda by means of a debate-based method delivered through one of three educational media: a) through a social role-playing game with competitive elements played on computers, b) through a very similar game played without computers and c) through a non-game workshop. Unlike many previous DGBL studies, this study used participant randomization and strived to address the teacher effect and the length of exposure effect, while also using the same learning materials and a very similar educational method for all three treatments. Both games induced comparatively higher generalized positive affect and flow. Participants also learned more with the games. Positive affect, but not flow, mediated the influence of educational media on learning gains. Participants’ competitiveness was partly related to positive affect and experiencing flow but unrelated to learning gains. These outcomes held both when the game was played using computers, as well as without them. The study indicates that the ability of an educational intervention to instigate positive affect is an important feature that should be considered by educational designers.

Fourier--type tests involving martingale difference processes

ABSTRACT We develop testing procedures which detect if the observed time series is a martingale difference sequence. Furthermore, tests are developed that detect change–points in the conditional expectation of the series given its past. The test statistics are formulated following the approach of Fourier–type conditional expectations first proposed by Bierens (1982) and have the advantage of computational simplicity. The limit behavior of the test statistics is investigated under the null hypothesis as well as under alternatives. Since the asymptotic null distribution contains unknown parameters, a bootstrap procedure is proposed in order to actually perform the test. The performance of the bootstrap version of the test is compared in finite samples with other methods for the same problem. A real–data application is also included.

Testing for spherical symmetry via the empirical characteristic function

Kolmogorov–Smirnov-type and Cramér–von Mises-type goodness-of-fit tests are proposed for the null hypothesis that the distribution of a random vector X is spherically symmetric. The test statistics utilize the fact that X has a spherical symmetric distribution if, and only if, the characteristic function of X is constant over surfaces of spheres centred at the origin. Both tests come in convenient forms that are straightforwardly applicable with the computer. The asymptotic null distribution of the test statistics as well as the consistency of the tests is investigated under general conditions. Since both the finite sample and the asymptotic null distribution depend on the unknown distribution of the Euclidean norm of X, a conditional Monte Carlo procedure is used to actually carry out the tests. Results on the behaviour of the test in finite-samples are included along with a real-data example.

Nonparametric Sequential Monitoring

Abstract The article concerns nonparametric sequential procedures for detection of instabilities in probability distribution in a series of observations. This is a partial survey of procedures based on either ranks, U-statistics, empirical distribution functions, or empirical characteristic functions. Most of the procedures assume that a training (historical) data set is available at the beginning of the monitoring. The main focus is on independent observations but extensions to time series are discussed. In order to derive properties of some procedures either the Anscombe theorem or its generalizations are applied. Most of the presented results can be extended to more general models.

Principal Component Analysis

This chapter addresses the issue of reducing the dimensionality of a multivariate random variable by using linear combinations (the principal components). The identified principal components are ordered in decreasing order of importance. When applied in practice to a data matrix, the principal components will turn out to be the factors of a transformed data matrix (the data will be centered and eventually standardized).

Does Motivation Enhance Knowledge Acquisition in Digital Game-Based and Multimedia Learning? A Review of Studies from One Lab

In the contexts of digital game-based and multimedia learning, little is known about the strengths of associations between positive affective-motivational factors elicited during a study session and the quality of knowledge acquisition. Here, we take a step forward in filling this gap by re-analyzing our 11 experiments carried out between 2009–2017, featuring digital games, a simulation, animations, or a computerized presentation (total N = 1,288; primarily Czech and Slovak high school and university learners). The correlational meta-analysis showed that the overall relationship between positive affective-motivational variables and learning outcomes was significant, but relatively weak. The weaker relationship was found for enjoyment and generalized positive affect compared to flow. The finding corroborates the idea that affective-motivational states may be differentially related to learning outcomes. Future research should investigate why some affective-motivational states seem to play relatively limited roles in learning from multimedia instructional materials.

Change Point Detection with Multivariate Observations Based on Characteristic Functions

We consider break-detection procedures for vector observations, both under independence as well as under an underlying structural time series scenario. The new methods involve L2-type criteria based on empirical characteristic functions. Asymptotic as well as Monte-Carlo results are presented. The new methods are also applied to time-series data from the financial sector.

Shape Constrained Regression in Sobolev Spaces with Application to Option Pricing

A class of nonparametric regression estimators based on penalized least squares over the sets of sufficiently smooth functions is elaborated. We impose additional shape constraint—isotonia—on the estimated regression curve and its derivatives. The problem of searching for the best fitting function in an infinite dimensional space is transformed into a finite dimensional optimization problem making this approach computationally feasible. The form and properties of the regression estimator in the Sobolev space are investigated. An application to option pricing is presented. The behavior of the estimator is improved by implementing an approximation of a covariance structure for the observed intraday option prices.

Highly Interactive, Computationally Intensive Techniques

Modern statistics is impossible without computers. The introduction of modern computers in the last quarter of the twentieth century created the subdiscipline “computational statistics.” This new science has subsequently initiated a variety of new computer-aided techniques. Some of these techniques, such as brushing of scatter plots, are highly interactive and computationally intensive.

Optimal designs for nonparametric estimation of zeros of regression functions

ABSTRACT We investigate nonparametric estimators of zeros of a regression function and its derivatives and we derive the distribution of design points minimizing the expected width of a confidence interval and the expected variance of the proposed estimator.