Introduction

Zadanie pt. „Digitalizacja i udostępnienie w Cyfrowym Repozytorium Uniwersytetu Łódzkiego kolekcji czasopism naukowych wydawanych przez Uniwersytet Łódzki” nr 885/P-DUN/2014 zostało dofinansowane ze środków MNiSW w ramach działalności upowszechniającej naukę

Econometrics: A bird's eye view

As a unified discipline, econometrics is still relatively young and has been transforming and expanding very rapidly over the past few decades. Major advances have taken place in the analysis of cross sectional data by means of semi-parametric and non-parametric techniques. Heterogeneity of economic relations across individuals, firms and industries is increasingly acknowledge and attempts have been made to take them into account either by integrating out their effects or by modeling the sources of heterogeneity when suitable panel data exists. The counterfactual considerations that underlie policy analysis and treatment evaluation have been given a more satisfactory foundation. New time series econometric techniques have been developed and employed extensively in the areas of macroeconometrics and finance. Non-linear econometric techniques are used increasingly in the analysis of cross section and time series observations. Applications of Bayesian techniques to econometric problems have been given new impetus largely thanks to advances in computer power and computational techniques. The use of Bayesian techniques have in turn provided the investigators with a unifying framework where the tasks and forecasting, decision making, model evaluation and learning can be considered as parts of the same interactive and iterative process; thus paving the way for establishing the foundation of the "real time econometrics". This paper attempts to provide an overview of some of these developments

Testing the isotropy of high energy cosmic rays using spherical needlets

For many decades, ultrahigh energy charged particles of unknown origin that can be observed from the ground have been a puzzle for particle physicists and astrophysicists. As an attempt to discriminate among several possible production scenarios, astrophysicists try to test the statistical isotropy of the directions of arrival of these cosmic rays. At the highest energies, they are supposed to point toward their sources with good accuracy. However, the observations are so rare that testing the distribution of such samples of directional data on the sphere is nontrivial. In this paper, we choose a nonparametric framework that makes weak hypotheses on the alternative distributions and allows in turn to detect various and possibly unexpected forms of anisotropy. We explore two particular procedures. Both are derived from fitting the empirical distribution with wavelet expansions of densities. We use the wavelet frame introduced by [SIAM J. Math. Anal. 38 (2006b) 574-594 (electronic)], the so-called needlets. The expansions are truncated at scale indices no larger than some ${J^{\star}}$, and the $L^p$ distances between those estimates and the null density are computed. One family of tests (called Multiple) is based on the idea of testing the distance from the null for each choice of $J=1,\ldots,{J^{\star}}$, whereas the so-called PlugIn approach is based on the single full ${J^{\star}}$ expansion, but with thresholded wavelet coefficients. We describe the practical implementation of these two procedures and compare them to other methods in the literature. As alternatives to isotropy, we consider both very simple toy models and more realistic nonisotropic models based on Physics-inspired simulations. The Monte Carlo study shows good performance of the Multiple test, even at moderate sample size, for a wide sample of alternative hypotheses and for different choices of the parameter ${J^{\star}}$. On the 69 most energetic events published by the Pierre Auger Collaboration, the needlet-based procedures suggest statistical evidence for anisotropy. Using several values for the parameters of the methods, our procedures yield $p$-values below 1%, but with uncontrolled multiplicity issues. The flexibility of this method and the possibility to modify it to take into account a large variety of extensions of the problem make it an interesting option for future investigation of the origin of ultrahigh energy cosmic rays.Comment: Published in at http://dx.doi.org/10.1214/12-AOAS619 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Multiple testing, uncertainty and realistic pictures

We study statistical detection of grayscale objects in noisy images. The object of interest is of unknown shape and has an unknown intensity, that can be varying over the object and can be negative. No boundary shape constraints are imposed on the object, only a weak bulk condition for the object's interior is required. We propose an algorithm that can be used to detect grayscale objects of unknown shapes in the presence of nonparametric noise of unknown level. Our algorithm is based on a nonparametric multiple testing procedure. We establish the limit of applicability of our method via an explicit, closed-form, non-asymptotic and nonparametric consistency bound. This bound is valid for a wide class of nonparametric noise distributions. We achieve this by proving an uncertainty principle for percolation on finite lattices.Comment: This paper initially appeared in January 2011 as EURANDOM Report 2011-004. Link to the abstract at EURANDOM Repository: http://www.eurandom.tue.nl/reports/2011/004-abstract.pdf Link to the paper at EURANDOM Repository: http://www.eurandom.tue.nl/reports/2011/004-report.pd

ecp: An R Package for Nonparametric Multiple Change Point Analysis of Multivariate Data

There are many different ways in which change point analysis can be performed, from purely parametric methods to those that are distribution free. The ecp package is designed to perform multiple change point analysis while making as few assumptions as possible. While many other change point methods are applicable only for univariate data, this R package is suitable for both univariate and multivariate observations. Estimation can be based upon either a hierarchical divisive or agglomerative algorithm. Divisive estimation sequentially identifies change points via a bisection algorithm. The agglomerative algorithm estimates change point locations by determining an optimal segmentation. Both approaches are able to detect any type of distributional change within the data. This provides an advantage over many existing change point algorithms which are only able to detect changes within the marginal distributions