Second order ancillary: A differential view from continuity

Second order approximate ancillaries have evolved as the primary ingredient for recent likelihood development in statistical inference. This uses quantile functions rather than the equivalent distribution functions, and the intrinsic ancillary contour is given explicitly as the plug-in estimate of the vector quantile function. The derivation uses a Taylor expansion of the full quantile function, and the linear term gives a tangent to the observed ancillary contour. For the scalar parameter case, there is a vector field that integrates to give the ancillary contours, but for the vector case, there are multiple vector fields and the Frobenius conditions for mutual consistency may not hold. We demonstrate, however, that the conditions hold in a restricted way and that this verifies the second order ancillary contours in moderate deviations. The methodology can generate an appropriate exact ancillary when such exists or an approximate ancillary for the numerical or Monte Carlo calculation of $p$-values and confidence quantiles. Examples are given, including nonlinear regression and several enigmatic examples from the literature.Comment: Published in at http://dx.doi.org/10.3150/10-BEJ248 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Three nontrivial solutions for nonlocal anisotropic inclusions under nonresonance

In this article, we study a pseudo-differential inclusion driven by a nonlocal anisotropic operator and a Clarke generalized subdifferential of a nonsmooth potential, which satisfies nonresonance conditions both at the origin and at infinity. We prove the existence of three nontrivial solutions: one positive, one negative and one of unknown sign, using variational methods based on nosmooth critical point theory, more precisely applying the second deformation theorem and spectral theory. Here, a nosmooth anisotropic version of the Hölder versus Sobolev minimizers relation play an important role

The Obstacle Problem at Zero for the Fractional p-Laplacian

In this paper we establish a multiplicity result for a class of unilateral, nonlinear, nonlocal problems with nonsmooth potential (variational-hemivariational inequalities), using the degree map of multivalued perturbations of fractional nonlinear operators of monotone type, the fact that the degree at a local minimizer of the corresponding Euler functional is equal one, and controlling the degree at small balls and at big balls

The obstacle problem at zero for the fractional p-Laplacian

In this paper we establish a multiplicity result for a class of unilateral, nonlinear, nonlocal problems with nonsmooth potential (variational-hemivariational inequalities), using the degree map of multivalued perturbations of fractional nonlinear operators of monotone type, the fact that the degree at a local minimizer of the corresponding Euler functional is equal one, and controlling the degree at small balls and at big balls.publishe

GENERALIZED MULTILEVEL FUNCTIONAL REGRESSION

We introduce Generalized Multilevel Functional Linear Models (GMFLM), a novel statistical framework motivated by and applied to the Sleep Heart Health Study (SHHS), the largest community cohort study of sleep. The primary goal of SHHS is to study the association between sleep disrupted breathing (SDB) and adverse health effects. An exposure of primary interest is the sleep electroencephalogram (EEG), which was observed for thousands of individuals at two visits, roughly 5 years apart. This unique study design led to the development of models where the outcome, e.g. hypertension, is in an exponential family and the exposure, e.g. sleep EEG, is multilevel functional data. We show that GMFLMs are, in fact, generalized multilevel mixed effect models. Two consequences of this result are that: 1) the mixed effects inferential machinery can be used for GMFLM and 2) functional regression models can be extended naturally to include, for example, additional covariates, random effects and nonparametric components. We propose and compare two inferential methods based on the parsimonious decomposition of the functional space

LIKELIHOOD RATIO TESTS FOR THE MEAN STRUCTURE OF CORRELATED FUNCTIONAL PROCESSES

The paper introduces a general framework for testing hypotheses about the structure of the mean function of complex functional processes. Important particular cases of the proposed framework are: 1) testing the null hypotheses that the mean of a functional process is parametric against a nonparametric alternative; and 2) testing the null hypothesis that the means of two possibly correlated functional processes are equal or differ by only a simple parametric function. A global pseudo likelihood ratio test is proposed and its asymptotic distribution is derived. The size and power properties of the test are confirmed in realistic simulation scenarios. Finite sample power results indicate that the proposed test is much more powerful than competing alternatives. Methods are applied to testing the equality between the means of normalized δ-power of sleep electroencephalograms of subjects with sleep-disordered breathing and matched controls

Search Based Clustering for Protecting Software with Diversified Updates

Reverse engineering is usually the stepping stone of a variety of attacks aiming at identifying sensitive information (keys, credentials, data, algorithms) or vulnerabilities and flaws for broader exploitation. Software applications are usually deployed as identical binary code installed on millions of computers, enabling an adversary to develop a generic reverse-engineering strategy that, if working on one code instance, could be applied to crack all the other instances. A solution to mitigate this problem is represented by Software Diversity, which aims at creating several structurally different (but functionally equivalent) binary code versions out of the same source code, so that even if a successful attack can be elaborated for one version, it should not work on a diversified version. In this paper, we address the problem of maximizing software diversity from a search-based optimization point of view. The program to protect is subject to a catalogue of transformations to generate many candidate versions. The problem of selecting the subset of most diversified versions to be deployed is formulated as an optimisation problem, that we tackle with different search heuristics. We show the applicability of this approach on some popular Android apps