A uniform functional law of the logarithm for the local empirical process

We prove a uniform functional law of the logarithm for the local empirical process. To accomplish this we combine techniques from classical and abstract empirical process theory, Gaussian distributional approximation and probability on Banach spaces. The body of techniques we develop should prove useful to the study of the strong consistency of d-variate kernel-type nonparametric function estimators.Comment: Published by the Institute of Mathematical Statistics (http://www.imstat.org) in the Annals of Probability (http://www.imstat.org/aop/) at http://dx.doi.org/10.1214/00911790400000024

Public opinion in Poland\u27s transition to market economy

Public opinion research has changed dramatically in the last ten years in Poland, in terms of its methodology, scope, and role in political change. During the first Solidarity era (1980–81), the genie of public opinion was let out of the bottle, and even martial law could not entirely put it back. Public opinion polling in the 1980s became more sophisticated and more common, and began to tackle increasingly sensitive political issues. Public opinion came to play a role in the political process, and to give the Polish population a sense of its own purpose and values. It also revealed the depth of antipathy to the communist regime and leadership and, in doing so, further eroded the already fragile legitimacy of the regime. When, in the late 1980s, the regime realized it could not succeed at winning back the allegiance, or at least acquiescence, of the Polish population, it agreed to negotiate with the opposition. The result was the emergence of the first noncommunist regime in Eastern Europe

Poland\u27s new trade unions

With the declaration of martial law in December 1981 and the formal banning of Solidarity in October 1982, the Polish regime created for itself a dilemma: how to provide a channel for participation by the workers without reactivating Solidarity and without allowing that participation to assume political dimensions. The Jaruzelski leadership professed a desire to achieve reconciliation and understanding in the aftermath of the heady days of Solidarity and the depressing denouement of martial law. One of the principal means to do this was through the creation of new institutions, allegedly independent, which would absorb some of the creative and participatory energy of Solidarity, without allowing a return to what the regime claimed had been political activities by the union

The U.S. No Longer Makes the Grade: Economic Inequality Put an End to the \u27American Century\u27

In his State of the Union address last January, U.S. President Barack Obama said that anyone who tells you that America is in decline or that our influence has waned, doesn\u27t know what they\u27re talking about. Former Utah Gov. Jon Huntsman, when in the race for the 2012 Republican presidential nomination, warned that unless Americans changed directions, they would see the end of the American century by 2015. As bright and capable as both of these politicians are, they are both whistling in the wind. The American century - the post-World War II era of U.S. global leadership and dominance - ended a decade ago, and it is not coming back. While that does not mean the cessation of American wealth and might, it does mark a significant transformation in U.S. society and economics, and the country\u27s place in the world. To cope with this transformation, Americans needs to recognize the nation\u27s relative decline

Ambitwistor strings and the scattering equations

We show that string theories admit chiral infinite tension analogues in which only the massless parts of the spectrum survive. Geometrically they describe holomorphic maps to spaces of complex null geodesics, known as ambitwistor spaces. They have the standard critical space--time dimensions of string theory (26 in the bosonic case and 10 for the superstring). Quantization leads to the formulae for tree--level scattering amplitudes of massless particles found recently by Cachazo, He and Yuan. These representations localize the vertex operators to solutions of the same equations found by Gross and Mende to govern the behaviour of strings in the limit of high energy, fixed angle scattering. Here, localization to the scattering equations emerges naturally as a consequence of working on ambitwistor space. The worldsheet theory suggests a way to extend these amplitudes to spinor fields and to loop level. We argue that this family of string theories is a natural extension of the existing twistor string theories.Comment: 31 pages + refs & appendice

Uniform in bandwidth consistency of kernel-type function estimators

We introduce a general method to prove uniform in bandwidth consistency of kernel-type function estimators. Examples include the kernel density estimator, the Nadaraya-Watson regression estimator and the conditional empirical process. Our results may be useful to establish uniform consistency of data-driven bandwidth kernel-type function estimators.Comment: Published at http://dx.doi.org/10.1214/009053605000000129 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Randomly Weighted Self-normalized L\'evy Processes

Let $(U_t,V_t)$ be a bivariate L\'evy process, where $V_t$ is a subordinator and $U_t$ is a L\'evy process formed by randomly weighting each jump of $V_t$ by an independent random variable $X_t$ having cdf $F$. We investigate the asymptotic distribution of the self-normalized L\'evy process $U_t/V_t$ at 0 and at $\infty$. We show that all subsequential limits of this ratio at 0 ($\infty$) are continuous for any nondegenerate $F$ with finite expectation if and only if $V_t$ belongs to the centered Feller class at 0 ($\infty$). We also characterize when $U_t/V_t$ has a non-degenerate limit distribution at 0 and $\infty$.Comment: 32 page

A note on a maximal Bernstein inequality

We show somewhat unexpectedly that whenever a general Bernstein-type maximal inequality holds for partial sums of a sequence of random variables, a maximal form of the inequality is also valid.Comment: Published in at http://dx.doi.org/10.3150/10-BEJ304 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm