On Relations Between the Relative entropy and χ2\chi^2-Divergence, Generalizations and Applications

The relative entropy and chi-squared divergence are fundamental divergence measures in information theory and statistics. This paper is focused on a study of integral relations between the two divergences, the implications of these relations, their information-theoretic applications, and some generalizations pertaining to the rich class of $f$-divergences. Applications that are studied in this paper refer to lossless compression, the method of types and large deviations, strong~data-processing inequalities, bounds on contraction coefficients and maximal correlation, and the convergence rate to stationarity of a type of discrete-time Markov chains.Comment: Published in the Entropy journal, May 18, 2020. Journal version (open access) is available at https://www.mdpi.com/1099-4300/22/5/56

The Effect of Motivation on Self-Employment Duration in Germany: Necessity versus Opportunity Entrepreneurs

Using data from the German Socio-Economic Panel Study (GSOEP), we analyze whether necessity and opportunity entrepreneurs differ in terms of self-employment duration. We find that the two types of entrepreneurs differ regarding their duration in self-employment. Once controlled for educational variables however, this effect turns out to be no longer significant. We therefore conclude that the difference observed is no original effect but is due to selection. We then go on to discuss the implications of our finding for entrepreneurship-policy making. Suggestions to improve governmental start-up support programmes are given. Estimations are carried out with discrete time hazard rate models controlling for unobserved heterogeneity.Self-employment; Firm survival; Necessity entrepreneurs; Opportunity entrepreneurs; Hazard rates; GSOEP

On the waiting time distribution for continuous stochastic systems

The waiting time distribution (WTD) is a common tool for analysing discrete stochastic processes in classical and quantum systems. However, there are many physical examples where the dynamics is continuous and only approximately discrete, or where it is favourable to discuss the dynamics on a discretized and a continuous level in parallel. An example is the hindered motion of particles through potential landscapes with barriers. In the present paper we propose a consistent generalisation of the WTD from the discrete case to situations where the particles perform continuous barrier-crossing characterised by a finite duration. To this end, we introduce a recipe to calculate the WTD from the Fokker-Planck/Smoluchowski equation. In contrast to the closely related first passage time distribution (FPTD), which is frequently used to describe continuous processes, the WTD contains information about the direction of motion. As an application, we consider the paradigmatic example of an overdamped particle diffusing through a washboard potential. To verify the approach and to elucidate its numerical implications, we compare the WTD defined via the Smoluchowski equation with data from direct simulation of the underlying Langevin equation and find full consistency provided that the jumps in the Langevin approach are defined properly. Moreover, for sufficiently large energy barriers, the WTD defined via the Smoluchowski equation becomes consistent with that resulting from the analytical solution of a (two-state) master equation model for the short-time dynamics developed previous by us [PRE 86, 061135 (2012)]. Thus, our approach "interpolates" between these two types of stochastic motion. We illustrate our approach for both symmetric systems and systems under constant force.Comment: 12 pages, 10 figure

Reading an academic expository text – The ESL learner’s experience

Researches on approaches to learning have often described students as either deep or surface learners. In essence, the deep approach is associated with intrinsic motivation, a focus on understanding the meaning of the learning material and relating new ideas to previous knowledge. In contrast, the surface approach views a particular task in isolation, a focus on memorizing discrete facts and reproduces terms through rote learning. Although these studies have provided information on the qualitative differences of learning in various contexts, little research has been conducted to examine the students’ learning approaches within an ESL context. Accordingly, the primary purpose of this paper is to describe and compare six ESL learners’ approaches of two readings of an academic expository text. Three instruments were used to collect data: reading sessions, individual interviews and observations, whereby all sessions were videotaped, audio taped and transcribed verbatim. Findings of the study revealed that there were qualitative differences in the ESL approaches of reading an academic expository text and that different types of approaches were employed in the two readings of the text. To conclude, the paper will further discuss the implications of the findings and some pedagogical considerations for the teaching and learning of reading within an ESL context

Two-Sided Search and Matching: Theory and Estimation

Frictions are a potentially important feature of many two-sided settings, for example, in the marriage market. My dissertation develops and estimates two-sided search and matching models and uses them to assess the importance of frictions in explaining observed marriage patterns. In the models, unmatched individuals search for long-term partners. Opportunities to meet potential partners arrive over time at uncertain intervals. Individuals are of different observable discrete types (e.g., gender and race/ethnicity) and types vary in their proportions within the population. Types may also differ in their type-pair specific utilities of marrying and their likelihood of meeting certain types of potential spouses. The first chapter in my dissertation proposes a new identification approach to separately estimate type-specific preferences and opportunities. I implement the technique to understand the marital patterns of racial and ethnic groups in the United States and to analyze the reasons for a high degree of same-type marriages. The second chapter theoretically analyzes the implications of the assumption that people prefer same-type partners. I show that frameworks with and without search frictions deliver different insights about the effects of group size on matching outcomes

Two Basic Methodological Choices in Wildland Vegetation Inventories: Their Consequences and Implications

In designing inventories of wildland vegetation, two of the many basic methodological choices are: 1) whether data are collected, reduced, and stored in discrete classes or as continuous variables, and 2) whether data are gathered as general purpose variables to bear upon many questions, or as specific purpose variables optimized for only one type of prediction. The effects of these two choices on accuracy of vegetation inventories to predict plant community production were examined by comparing regression models built upon differing sets of independent variables inventoried from a common data base. Contrary to expectations, discrete variables of classified community types were better predictors of plant community production than the same vegetation data reduced as continuous variables by three ordination techniques. Substitution of specific purpose soil and vegetation variables thought to be especially relevant to production did not improve correlations from those of analogous general purpose variables. These results do not show the anticipated accuracy loss of general purpose inventory variables, but such findings cannot yet be generalized to other situations. Implications for the design of practical, extensive survey methods for wildland vegetation are briefly discussed