Bootstrap inference in the presence of bias

We consider bootstrap inference for estimators which are (asymptotically) biased. We show that, even when the bias term cannot be consistently estimated, valid inference can be obtained by proper implementations of the bootstrap. Specifically, we show that the prepivoting approach of Beran (1987, 1988), originally proposed to deliver higher-order refinements, restores bootstrap validity by transforming the original bootstrap p-value into an asymptotically uniform random variable. We propose two different implementations of prepivoting (plug-in and double bootstrap), and provide general high-level conditions that imply validity of bootstrap inference. To illustrate the practical relevance and implementation of our results, we discuss five applications: (i) a simple location model for i.i.d. data, possibly with infinite variance; (ii) regression models with omitted controls; (iii) inference on a target parameter based on model averaging; (iv) ridge-type regularized estimators; and (v) dynamic panel data models

Features of collisionless turbulence in the intracluster medium from simulated Faraday Rotation maps

Observations of the intracluster medium (ICM) in galaxy clusters suggest for the presence of turbulence and the magnetic fields existence has been proved through observations of Faraday Rotation and synchrotron emission. The ICM is also known to be filled by a rarefied weakly collisional plasma. In this work we study the possible signatures left on Faraday Rotation maps by collisionless instabilities. For this purpose we use a numerical approach to investigate the dynamics of the turbulence in collisionless plasmas based on an magnetohydrodynamical (MHD) formalism taking into account different levels of pressure anisotropy. We consider models covering the sub/super-Alfv\'enic and trans/supersonic regimes, one of them representing the fiducial conditions corresponding to the ICM. From the simulated models we compute Faraday Rotation maps and analyze several statistical indicators in order to characterize the magnetic field structure and compare the results obtained with the collisionless model to those obtained using standard collisional MHD framework. We find that important imprints of the pressure anisotropy prevails in the magnetic field and also manifest in the associated Faraday Rotation maps which evidence smaller correlation lengths in the collisionless MHD case. These points are remarkably noticeable for the case mimicking the conditions prevailing in ICM. Nevertheless, in this study we have neglected the decrease of pressure anisotropy due to the feedback of the instabilities that naturally arise in collisionless plasmas at small scales. This decrease may not affect the statistical imprint differences described above, but should be examined elsewhere.Comment: 24 pages, 15 figures, MNRAS accepte

The Domination Number of Grids

In this paper, we conclude the calculation of the domination number of all $n\times m$ grid graphs. Indeed, we prove Chang's conjecture saying that for every $16\le n\le m$, $\gamma(G_{n,m})=\lfloor\frac{(n+2)(m+2)}{5}\rfloor -4$.Comment: 12 pages, 4 figure

Hysteretic Optimization For Spin Glasses

The recently proposed Hysteretic Optimization (HO) procedure is applied to the 1D Ising spin chain with long range interactions. To study its effectiveness, the quality of ground state energies found as a function of the distance dependence exponent, $\sigma$, is assessed. It is found that the transition from an infinite-range to a long-range interaction at $\sigma=0.5$ is accompanied by a sharp decrease in the performance . The transition is signaled by a change in the scaling behavior of the average avalanche size observed during the hysteresis process. This indicates that HO requires the system to be infinite-range, with a high degree of interconnectivity between variables leading to large avalanches, in order to function properly. An analysis of the way auto-correlations evolve during the optimization procedure confirm that the search of phase space is less efficient, with the system becoming effectively stuck in suboptimal configurations much earlier. These observations explain the poor performance that HO obtained for the Edwards-Anderson spin glass on finite-dimensional lattices, and suggest that its usefulness might be limited in many combinatorial optimization problems.Comment: 6 pages, 9 figures. To appear in JSTAT. Author website: http://www.bgoncalves.co

Qualitative analysis of a scalar-tensor theory with exponential potential

A qualitative analysis of a scalar-tensor cosmological model, with an exponential potential for the scalar field, is performed. The phase diagram for the flat case is constructed. It is shown that solutions with an initial and final inflationary behaviour appear. The conditions for which the scenario favored by supernova type Ia observations becomes an attractor in the space of the solutions are established.Comment: Latex file, 9 pages, 1 figur

Alterações nos atributos químicos do solo proveniente da adição de fontes alternativas portadoras de potássio.

Dada a enorme geodiversidade que ocorre no Brasil, a tecnologia da aplicação de pó de rocha (rochagem) configura-se como uma excelente alternativa ao fornecimento de nutrientes no solo. Objetivou-se avaliar os efeitos de fontes alternativas de nutrientes nos atributos químicos do solo em um experimento de incubação realizado em casa de vegetação. Foi conduzido em vasos com 5 kg preenchidos com um Latossolo Vermelho Amarelo distrófico de textura média, com teor de K (Mehlich-1) de 0,06 cmolc dm-3 de solo. O delineamento experimental foi inteiramente casualizado e os tratamentos foram distribuídos em arranjo fatorial 5 x 9 x 3, sendo cinco doses de potássio (0, 150, 300, 450 e 600 kg ha-1 de K2O) e nove fontes alternativas de nutrientes (verdete, 25C:75V, verdete tratado com NH4OH, ultramáfica, 25C:75U, fonolito, 25C:75F, resíduo de mineração, 25C:75R), com três repetições. As fontes alternativas de nutrientes foram aplicadas e incorporadas ao solo, deixando-os em incubação por um período de 45 dias, com a umidade em torno de 70% da capacidade de campo, e, após isto, foram feitas análises do solo. Os fertilizantes potássicos alteraram a disponibilidade de nutrientes, sendo que o resíduo de mineração e sua mistura foram os que mais liberaram K para o solo em todas as doses testadas