Domenico Marinucci

Semiparametric fractional cointegration analysis

Fractional cointegration is viewed from a semiparametric viewpoint as a narrow-band phenomenon at frequency zero. We study a narrow-band frequency domain least squares estimate of the cointegrating vector, and related semiparametric methods of inference for testing the memory of observables and the presence of fractional cointegration. These procedures are employed in analysing empirical macroeconomic series; their usefulness and feasibility in finite samples is supported by results of a Monte Carlo experiment.

Weak convergence of multivariate fractional processes

Weak convergence to a form of fractional Brownian motion is established for a wide class of nonstationary fractionally integrated multivariate processes. Instrumental for the main argument is a result of some independent interest on approximations for partial sums of stationary linear vector sequences. A functional central limit theorem for smoothed processes is established under more general assumptions.

A statistical procedure for the identification of positrons in the PAMELA experiment

The PAMELA satellite experiment has measured the cosmic-ray positron fraction between 1.5 GeV and 100 GeV. The need to reliably discriminate between the positron signal and proton background has required the development of an ad hoc analysis procedure. In this paper, a method for positron identification is described and its stability and capability to yield a correct background estimate is shown. The analysis includes new experimental data, the application of three different fitting techniques for the background sample and an estimate of systematic uncertainties due to possible inaccuracies in the background selection. The new experimental results confirm both solar modulation effects on cosmic-rays with low rigidities and an anomalous positron abundance above 10 GeV.

Asymmetries in the Local Curvature of the Wilkinson Microwave Anisotropy Probe Data

We use the local curvature to investigate the possible existence of non-Gaussianity/asymmetry in the Wilkinson Microwave Anisotropy Probe data. Considering the full sky, we find results that are consistent with the Gaussian assumption. However, strong non-Gaussian features emerge when considering the northern and southern Galactic hemisphere separately, particularly on scales between 1° and 5°. Quite interestingly, the maximum non-Gaussianity is found for hemispheres centered near the ecliptic poles, which might suggest the presence of some systematic effect. The direction of the asymmetry seems consistent with the findings by Eriksen et al.We use the local curvature to investigate the possible existence of non-Gaussianity/asymmetry in the WMAP data. Considering the full sky we find results which are consistent with the Gaussian assumption. However, strong non-Gaussian features emerge when considering the northern and southern galactic hemisphere separately, particularly on scales between 1 and 5 degrees. Quite interestingly, the maximum non-Gaussianity is found for hemispheres centered near the ecliptic poles, which might suggest the presence of some systematic effect. The direction of the asymmetry seems consistent with the findings by Eriksen et al. 2004. Subject headings: (cosmology:) cosmic microwave background — cosmology: observations — methods: data analysis — methods: statistical

Asymptotics for spherical needlets

We investigate invariant random fields on the sphere using a new type of spherical wavelets, called needlets. These are compactly supported in frequency and enjoy excellent localization properties in real space, with quasi-exponentially decaying tails. We show that, for random fields on the sphere, the needlet coefficients are asymptotically uncorrelated for any fixed angular distance. This property is used to derive CLT and functional CLT convergence results for polynomial functionals of the needlet coefficients: here the asymptotictheory is considered in the high-frequency sense. Our proposals emerge from strong empirical motivations, especially in connection with the analysis of cosmological data sets. 1. Introduction. Over the last two decades, wavelets have emerged as one of the most interesting tools of statistical investigation. In this paper we give an application to the statistical analysis of data sets indexed by the unit sphere S 2 . This is motivated mostly by the analysis of the Cosmic

An Estimate of the Primordial Non-Gaussianity Parameter f_NL Using the Needlet Bispectrum from WMAP

We use the full bispectrum of spherical needlets applied to the WMAP data of the cosmic microwave background as an estimator for the primordial non-Gaussianity parameter fNL. We use needlet scales up to lmax = 1000 and the KQ75 galactic cut and find fNL = 84 ± 40 corrected for point source bias. We also introduce a set of consistency tests to validate our results against the possible influence of foreground residuals or systematic errors. In particular, fluctuations in the value of fNL obtained from different frequency channels, different masks and different multipoles are tested against simulated maps. All variations in fNL estimates are found statistically consistent with simulations. Subject headings: cosmic microwave background — cosmology: observations — methods: statistical

Subsampling Needlet Coefficients on the Sphere

In a recent paper, we analyzed the properties of a new kind of spherical wavelets (so-called needlets) for statistical inference procedures on spherical random fields; the results were mainly motivated by applications to cosmological data. In the present work, we exploit the asymptotic uncorrelation of random needlet coefficients at fixed angular distances to construct subsampling statistics evaluated on Voronoi cells on the sphere. We illustrate how such statistics can be used for isotropy tests and for bootstrap estimation of nuisance parameters, even when a single realization of the spherical random field is observed. The asymptotic theory is developed in details, in the high resolution sense.

Adaptive density estimation for directional data using needlets

This paper is concerned with density estimation of directional data on the sphere. We introduce a procedure based on thresholding on a new type of spherical wavelets called {\it needlets}. We establish a minimax result and prove its optimality. We are motivated by astrophysical applications, in particular in connection with the analysis of ultra high energy cosmic rays.

High-resolution asymptotics for the angular bispectrum of spherical random fields

In this paper we study the asymptotic behavior of the angular bispectrum of spherical random fields. Here, the asymptotic theory is developed in the framework of fixed-radius fields, which are observed with increasing resolution as the sample size grows. The results we present are then exploited in a set of procedures aimed at testing non-Gaussianity; for these statistics, we are able to show convergence to functionals of standard Brownian motion under the null hypothesis. Analytic results are also presented on the behavior of the tests in the presence of a broad class of non-Gaussian alternatives. The issue of testing for non-Gaussianity on spherical random fields has recently gained enormous empirical importance, especially in connection with the statistical analysis of cosmic microwave background radiation.

The needlets bispectrum

The purpose of this paper is to join two different threads of the recent literature on random fields on the sphere, namely the statisti- cal analysis of higher order angular power spectra on one hand, and the construction of second-generation wavelets on the sphere on the other. To this aim, we introduce the needlets bispectrum and we derive a number of convergence results. Here, the limit theory is developed in the high resolu- tion sense. The leading motivation of these results is the need for statistical procedures for searching non-Gaussianity in Cosmic Microwave Background radiation. AMS 2000 subject classifications: Primary 62G20; secondary 62M15, 60B15, 60G60. Keywords and phrases: Bispectrum, Needlets, Spherical Random Fields, Cosmic Microwave Background Radiation, High Resolution Asymptotics.