Dynamic Analysis of a Unified Multivariate Counting Process and Its Asymptotic Behavior

The class of counting processes constitutes a significant part of applied probability. The classic counting processes include Poisson processes, nonhomogeneous Poisson processes, and renewal processes. More sophisticated counting processes, including Markov renewal processes, Markov modulated Poisson processes, age-dependent counting processes, and the like, have been developed for accommodating a wider range of applications. These counting processes seem to be quite different on the surface, forcing one to understand each of them separately. The purpose of this paper is to develop a unified multivariate counting process, enabling one to express all of the above examples using its components, and to introduce new counting processes. The dynamic behavior of the unified multivariate counting process is analyzed, and its asymptotic behavior as t→∞ is established. As an application, a manufacturing system with certain maintenance policies is considered, where the optimal maintenance policy for minimizing the total cost is obtained numerically

Forbidden ordinal patterns in higher dimensional dynamics

Forbidden ordinal patterns are ordinal patterns (or `rank blocks') that cannot appear in the orbits generated by a map taking values on a linearly ordered space, in which case we say that the map has forbidden patterns. Once a map has a forbidden pattern of a given length $L_{0}$, it has forbidden patterns of any length $L\ge L_{0}$ and their number grows superexponentially with $L$. Using recent results on topological permutation entropy, we study in this paper the existence and some basic properties of forbidden ordinal patterns for self maps on n-dimensional intervals. Our most applicable conclusion is that expansive interval maps with finite topological entropy have necessarily forbidden patterns, although we conjecture that this is also the case under more general conditions. The theoretical results are nicely illustrated for n=2 both using the naive counting estimator for forbidden patterns and Chao's estimator for the number of classes in a population. The robustness of forbidden ordinal patterns against observational white noise is also illustrated.Comment: 19 pages, 6 figure

In Search of Leading Indicators of Economic Activity in Germany

In this paper we present two new composite leading indicators of economicactivity in Germany estimated using a dynamic factor model with and withoutregime switching. The obtained optimal inferences of business cycle turningpoints indicate that the two-state regime switching procedure leads to asuccessful representation of the sample data and provides an appropriatetool for forecasting business conditions.business cycles, leading indicators, turning points, Markovswitching, Germany

A unified approach to linear probing hashing with buckets

We give a unified analysis of linear probing hashing with a general bucket size. We use both a combinatorial approach, giving exact formulas for generating functions, and a probabilistic approach, giving simple derivations of asymptotic results. Both approaches complement nicely, and give a good insight in the relation between linear probing and random walks. A key methodological contribution, at the core of Analytic Combinatorics, is the use of the symbolic method (based on q-calculus) to directly derive the generating functions to analyze.Comment: 49 page

Bayesian and Non-Bayesian Approaches to Scientific Modeling and Inference in Economics and Econometrics

After brief remarks on the history of modeling and inference techniques in economics and econometrics , attention is focused on the emergence of economic science in the 20th century. First, the broad objectives of science and the Pearson-Jeffreys' "unity of science" principle will be reviewed. Second, key Bayesian and non-Bayesian practical scientific inference and decision methods will be compared using applied examples from economics, econometrics and business. Third, issues and controversies on how to model the behavior of economic units and systems will be reviewed and the structural econometric modeling, time series analysis (SEMTSA) approach will be described and illustrated using a macro-economic modeling and forecasting problem involving analyses of data for 18 industrialized countries over the years since the 1950s. Point and turning point forecasting results will be summarized. Last, a few remarks will be made about the future of scientific inference and modeling techniques in economics and econometrics.

Models for Paired Comparison Data: A Review with Emphasis on Dependent Data

Thurstonian and Bradley-Terry models are the most commonly applied models in the analysis of paired comparison data. Since their introduction, numerous developments have been proposed in different areas. This paper provides an updated overview of these extensions, including how to account for object- and subject-specific covariates and how to deal with ordinal paired comparison data. Special emphasis is given to models for dependent comparisons. Although these models are more realistic, their use is complicated by numerical difficulties. We therefore concentrate on implementation issues. In particular, a pairwise likelihood approach is explored for models for dependent paired comparison data, and a simulation study is carried out to compare the performance of maximum pairwise likelihood with other limited information estimation methods. The methodology is illustrated throughout using a real data set about university paired comparisons performed by students.Comment: Published in at http://dx.doi.org/10.1214/12-STS396 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Great Expectatrics: Great Papers, Great Journals, Great Econometrics

The paper discusses alternative Research Assessment Measures (RAM), with an emphasis on the Thomson Reuters ISI Web of Science database (hereafter ISI). The various ISI RAM that are calculated annually or updated daily are defined and analysed, including the classic 2-year impact factor (2YIF), 5-year impact factor (5YIF), Immediacy (or zero-year impact factor (0YIF)), Eigenfactor score, Article Influence, C3PO (Citation Performance Per Paper Online), h-index, Zinfluence, and PI-BETA (Papers Ignored - By Even The Authors). The ISI RAM data are analysed for 8 leading econometrics journals and 4 leading statistics journals. The application to econometrics can be used as a template for other areas in economics, for other scientific disciplines, and as a benchmark for newer journals in a range of disciplines. In addition to evaluating high quality research in leading econometrics journals, the paper also compares econometrics and statistics, alternative RAM, highlights the similarities and differences in alternative RAM criteria, finds that several ISI RAM capture similar performance characteristics for the leading econometrics and statistics journals while the new PI-BETA criterion is not highly correlated with any of the other ISI RAM, and hence conveys additional information regarding ISI RAM, highlights major research areas in leading journals in econometrics, and discusses some likely future uses of RAM.Research assessment measures; impact factors; Immediacy; Eigenfactor score; Article influence; h-index; C3PO; Zinfluence; PI-BETA