Central limit theorems for Poisson hyperplane tessellations

We derive a central limit theorem for the number of vertices of convex polytopes induced by stationary Poisson hyperplane processes in $\mathbb{R}^d$. This result generalizes an earlier one proved by Paroux [Adv. in Appl. Probab. 30 (1998) 640--656] for intersection points of motion-invariant Poisson line processes in $\mathbb{R}^2$. Our proof is based on Hoeffding's decomposition of $U$-statistics which seems to be more efficient and adequate to tackle the higher-dimensional case than the ``method of moments'' used in [Adv. in Appl. Probab. 30 (1998) 640--656] to treat the case $d=2$. Moreover, we extend our central limit theorem in several directions. First we consider $k$-flat processes induced by Poisson hyperplane processes in $\mathbb{R}^d$ for $0\le k\le d-1$. Second we derive (asymptotic) confidence intervals for the intensities of these $k$-flat processes and, third, we prove multivariate central limit theorems for the $d$-dimensional joint vectors of numbers of $k$-flats and their $k$-volumes, respectively, in an increasing spherical region.Comment: Published at http://dx.doi.org/10.1214/105051606000000033 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Limit theorems for functionals on the facets of stationary random tessellations

We observe stationary random tessellations $X=\{\Xi_n\}_{n\ge1}$ in $\mathbb{R}^d$ through a convex sampling window $W$ that expands unboundedly and we determine the total $(k-1)$-volume of those $(k-1)$-dimensional manifold processes which are induced on the $k$-facets of $X$ ($1\le k\le d-1$) by their intersections with the $(d-1)$-facets of independent and identically distributed motion-invariant tessellations $X_n$ generated within each cell $\Xi_n$ of $X$. The cases of $X$ being either a Poisson hyperplane tessellation or a random tessellation with weak dependences are treated separately. In both cases, however, we obtain that all of the total volumes measured in $W$ are approximately normally distributed when $W$ is sufficiently large. Structural formulae for mean values and asymptotic variances are derived and explicit numerical values are given for planar Poisson--Voronoi tessellations (PVTs) and Poisson line tessellations (PLTs).Comment: Published at http://dx.doi.org/10.3150/07-BEJ6131 in the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

The new keynesian approach to dynamic general equilibrium modeling: models, methods, and macroeconomic policy evaluation

This chapter aims to provide a hands-on approach to New Keynesian models and their uses for macroeconomic policy analysis. It starts by reviewing the origins of the New Keynesian approach, the key model ingredients and representative models. Building blocks of current-generation dynamic stochastic general equilibrium (DSGE) models are discussed in detail. These models address the famous Lucas critique by deriving behavioral equations systematically from the optimizing and forward-looking decision-making of households and firms subject to well-defined constraints. State-of-the-art methods for solving and estimating such models are reviewed and presented in examples. The chapter goes beyond the mere presentation of the most popular benchmark model by providing a framework for model comparison along with a database that includes a wide variety of macroeconomic models. Thus, it offers a convenient approach for comparing new models to available benchmarks and for investigating whether particular policy recommendations are robust to model uncertainty. Such robustness analysis is illustrated by evaluating the performance of simple monetary policy rules across a range of recently-estimated models including some with financial market imperfections and by reviewing recent comparative findings regarding the magnitude of government spending multipliers. The chapter concludes with a discussion of important objectives for on-going and future research using the New Keynesian framework

Asymptotic goodness-of-fit tests for the Palm mark distribution of stationary point processes with correlated marks

We consider spatially homogeneous marked point patterns in an unboundedly expanding convex sampling window. Our main objective is to identify the distribution of the typical mark by constructing an asymptotic $\chi^2$-goodness-of-fit test. The corresponding test statistic is based on a natural empirical version of the Palm mark distribution and a smoothed covariance estimator which turns out to be mean square consistent. Our approach does not require independent marks and allows dependences between the mark field and the point pattern. Instead we impose a suitable $\beta$-mixing condition on the underlying stationary marked point process which can be checked for a number of Poisson-based models and, in particular, in the case of geostatistical marking. In order to study test performance, our test approach is applied to detect anisotropy of specific Boolean models.Comment: Published in at http://dx.doi.org/10.3150/13-BEJ523 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm). arXiv admin note: substantial text overlap with arXiv:1205.504

Multiple modernities? The case against

"The paper rejects the notion of 'multiple modernities' as both conceptually flawed and empirically unfounded. In line with the sociological tradition, it will argue that we should speak of modernity only in the singular. Modernity, according to this view, denotesa peculiar epoch in the history of human kind, originating in Europe and spreading from there to the rest of the world. We may well be tempted to succumb too quickly to ill-conceived generalizations of what are in fact often only particular, locally based experiences. But we should also not lose sight of the truly revolutionary character of the historical 'breakthrough' to modernity. The protagonists of the multiple modernities paradigm appear to be doing precisely this: their very terminology impliesa trivialization of what is common to 'the' modern condition. At the same time, it suggests an overrating of which ever diversities (may) exist in different parts of the world. The paper will identify four main conceptual flaws in the pertinent literature: 1. The proclivity to equate modernity with its polity. The proposed conception of modernity is thus too thin for capturing the complex social structure of modern society as a whole. 2. To the extent that a theory of modernity is proposed at all, this theory is a self proclaimed cultural theory. Such a theory may shed light on some of the historical roots and self-perceptions of modernity, but it does so at the cost of excluding any thorough analysis of institutions. 3. The conceptualization of inter-societal difference in civilizational terms is misleading because it rules out, almost by definition, the possibility that countries belonging to different civilizations may in certain respects have more in common with ones from other civilizations than with some of the members of their 'own'. 4. The account's notion of diversity is exceedingly vague - the nature and profundity of the differences that are said to exist between different modernities are nowhere discussed at adequate length. But we need to know them to assess their social theoretic significance. In addition to these conceptual flaws, there are also various empirical phenomena and trends that challenge key premises of the multiple modernities approach. None of this is to say there are no differences between different regions, countries, civilizations. Nor is it to suggest their insignificance. It is, however, to suggest that we be more precise and that we extend our analyses beyond the confines of culture and politics - at least if we want to say something meaningful about modernity or modern society at large. Rather than speaking of multiple modernities, a better alternative to accommodate existing differences might be a yet to be developed concept of 'varieties of modernity' - akin to (but naturally pitched at a higher level of abstraction than) the notion of 'varieties of capitalism' which is beginning to crystallize in the new political economy literature." (author's abstract

What's wrong with the concept of multiple modernities?

The concept of multiple modernities has been developed with a view to highlighting the ways in which modern societies differ from each other. Other sociological approaches, by contrast, emphasize such societies' commonalities. But does the juxtaposition of convergence and divergence in the form of a mutually exclusive, binary opposition really make sense? Might it be that there is convergence in some respect, while diversity persists in other respects; that there are dimensions of social change that exhibit common trends across regions and cultural zones, while other aspects of social life show remarkable resilience against homogenization? The present paper argues that our observation of convergence or diversity might be less a matter of truth or falsity than an artifact of our chosen methodologies. Based on this premise, the concept of multiple modernities will be rejected as sociologically meaningless, conceptually flawed and empirically dubious. It is sociologically meaningless because its advocates fail to spell out sufficiently clearly what they mean by modern as against non-modern societies; it is conceptually flawed because it does not provide criteria for distinguishing theoretically significant from insignificant (or less significant) differences, and it is empirically dubious because it misrepresents the state of the world's development

Limits to growth? China's rise and its implications for Europe

"The paper outlines two future scenarios, one 'pessimistic', the other more 'optimistic'. The first assumes that definite limits to growth exist and that, to the extent that this is still possible, economic policies must be radically altered to prevent the collapse of our ecosystems ('global warming'). If this assessment were correct, then we would probably be doomed. For even if all understood the dangers, it would still seem to be extremely unlikely that the major world powers will exit the market economy, i.e. an economic system premised on perpetual growth, anytime soon. Because such a scenario, while possibly realistic, would be social scientifically sterile (why bother if the world is going bust anyway?), the second scenario construes a somewhat 'friendlier' outlook of the future, one in which technologies become available that render economic growth and ecological sustainability compatible. If this scenario came true, then where would the world be headed in the 21st century? This is the question I wish to pursue here, with special emphasis given to China's rise and its implications for Europe. During the past 27 years, China's economy exhibited an average annual growth of 9.6%. At this rate of growth, a country doubles its income every 7.5 years. That means a child born in China today grows up in a country that is 12 times richer than it was during the youth of his/ her parents. If this growth continues unabated, as economist believe it can for at least several more years, then China will overtake the US as the world's largest economy by 2020. At that point, China's per capita incomes would still be below the OECD average. But the world would already have witnessed the emergence of an economic giant of historically unprecedented proportions. And this giant would still have ample scope for further catching up. Given that China's population is more than double that of the whole West, a China that reached a level of development similar to that of an average OECD member would dwarf any single European economy and, eventually, surpass the economies of North America and Europe combined. This would not only shift the weights in the world economy, but sooner or later also those in world politics, in military strength, and, potentially, in the areas of science and (popular) culture as well. At the present point in time, nobody can say with certainty whether any of this will come true. But if it did, then it would mean nothing less than the end of an era that lasted for about 500 years: the era of uncontested European or, for that matter, Western supremacy. Since China is not the only newly emerging power (as is well known, India and Brazil are rapidly rising too now), such a development would seem to be all the more likely. Thus far, however, Europeans appear to be largely oblivious to it. Remarkably, this is true even of the continent's leading intellectual circles. They had better attend to the matter and prepare their publics." (author's abstract