On maxitive integration

The Shilkret integral is maxitive (i.e., the integral of a pointwise supremum of functions is the supremum of their integrals), but defined only for nonnegative functions. In the present paper, some properties of this integral (such as subadditivity and a law of iterated expectations) are studied, in comparison with the additive and Choquet integrals. Furthermore, the definition of a maxitive integral for all real functions is discussed. In particular, a convex, maxitive integral is introduced and some of its properties are derived

On maxitive integration

A functional is said to be maxitive if it commutes with the (pointwise) supremum operation. Such functionals find application in particular in decision theory and related fields. In the present paper, maxitive functionals are characterized as integrals with respect to maxitive measures (also known as possibility measures or idempotent measures). These maxitive integrals are then compared with the usual additive and nonadditive integrals on the basis of some important properties, such as convexity, subadditivity, and the law of iterated expectations

Likelihood decision functions

In both classical and Bayesian approaches, statistical inference is unified and generalized by the corresponding decision theory. This is not the case for the likelihood approach to statistical inference, in spite of the manifest success of the likelihood methods in statistics. The goal of the present work is to fill this gap, by extending the likelihood approach in order to cover decision making as well. The resulting decision functions, called likelihood decision functions, generalize the usual likelihood methods (such as ML estimators and LR tests), in the sense that these methods appear as the likelihood decision functions in particular decision problems. In general, the likelihood decision functions maintain some key properties of the usual likelihood methods, such as equivariance and asymptotic optimality. By unifying and generalizing the likelihood approach to statistical inference, the present work offers a new perspective on statistical methodology and on the connections among likelihood methods

The Quest for Bandwidth Estimation Techniques for large-scale Distributed Systems

In recent years the research community has developed many techniques to estimate the end-to-end available bandwidth of an Internet path. This important metric has been proposed for use in several distributed systems and, more recently, has even been considered to improve the congestion control mechanism of TCP. Thus, it has been suggested that some existing estimation techniques could be used for this purpose. However, existing tools were not designed for large-scale deployments and were mostly validated in controlled settings, considering only one measurement running at a time. In this paper, we argue that current tools, while offering good estimates when used alone, might not work in large-scale systems where several estimations severely interfere with each other. We analyze the properties of the measurement paradigms employed today and discuss their functioning, study their overhead and analyze their interference. Our testbed results show that current techniques are insufficient as they are. Finally, we will discuss and propose some principles that should be taken into account for including available bandwidth measurements in large-scale distributed systems. 1

Robust regression with imprecise data

We consider the problem of regression analysis with imprecise data. By imprecise data we mean imprecise observations of precise quantities in the form of sets of values. In this paper, we explore a recently introduced likelihood-based approach to regression with such data. The approach is very general, since it covers all kinds of imprecise data (i.e. not only intervals) and it is not restricted to linear regression. Its result consists of a set of functions, reflecting the entire uncertainty of the regression problem. Here we study in particular a robust special case of the likelihood-based imprecise regression, which can be interpreted as a generalization of the method of least median of squares. Moreover, we apply it to data from a social survey, and compare it with other approaches to regression with imprecise data. It turns out that the likelihood-based approach is the most generally applicable one and is the only approach accounting for multiple sources of uncertainty at the same time

A non-parametric microsimulation approach to assess changes in inequality and poverty

This paper presents a non-parametric microsimulation methodology for assessing the impact of labour market changes and government transfers on income inequality and poverty at the household level. The approach assumes that labour markets are segmented and determines (as part of a randomized process) which individuals are expected to move in or out of employment and which move from one employment segment to another based on either known or counterfactual information of aggregate labour market changes. The methodology assumes that the distribution of earnings of those who become employed in a particular segment resembles that of the individuals observed to be employed in that segment. The approach can be effectively combined in top-down fashion with static or dynamic computable general equilibrium (CGE) models, which typically provide insufficient information about household income distribution. The paper discusses the virtues and limitations of applying this methodology and further explains to practitioners how to implement it as a stand-alone methodology or in combination with a CGE model. It also shows how the methodology can be generalized to also capture the poverty and inequality effects of changes in non-labour incomes, such as government transfers. One great advantage of this method is that it is not very demanding in terms of modelling labour supply and household behaviour as compared with alternative parametric approaches, while at the same time providing a plausible link between changes in overall labour market conditions and the full household income distribution.

On the implementation of LIR: the case of simple linear regression with interval data

This paper considers the problem of simple linear regression with interval-censored data. That is, n pairs of intervals are observed instead of the n pairs of precise values for the two variables (dependent and independent). Each of these intervals is closed but possibly unbounded, and contains the corresponding (unobserved) value of the dependent or independent variable. The goal of the regression is to describe the relationship between (the precise values of) these two variables by means of a linear function. Likelihood-based Imprecise Regression (LIR) is a recently introduced, very general approach to regression for imprecisely observed quantities. The result of a LIR analysis is in general set-valued: it consists of all regression functions that cannot be excluded on the basis of likelihood inference. These regression functions are said to be undominated. Since the interval data can be unbounded, a robust regression method is necessary. Hence, we consider the robust LIR method based on the minimization of the residuals' quantiles. For this method, we prove that the set of all the intercept-slope pairs corresponding to the undominated regression functions is the union of finitely many polygons. We give an exact algorithm for determining this set (i.e., for determining the set-valued result of the robust LIR analysis), and show that it has worst-case time complexity O(n^3 log n). We have implemented this exact algorithm as part of the R package linLIR

Recurrence for persistent random walks in two dimensions

We discuss the question of recurrence for persistent, or Newtonian, random walks in Z^2, i.e., random walks whose transition probabilities depend both on the walker's position and incoming direction. We use results by Toth and Schmidt-Conze to prove recurrence for a large class of such processes, including all "invertible" walks in elliptic random environments. Furthermore, rewriting our Newtonian walks as ordinary random walks in a suitable graph, we gain a better idea of the geometric features of the problem, and obtain further examples of recurrence.Comment: 20 pages, 7 figure

On Integrability of spinning particle motion in higher-dimensional black hole spacetimes

We study the motion of a classical spinning particle (with spin degrees of freedom described by a vector of Grassmann variables) in higher-dimensional general rotating black hole spacetimes with a cosmological constant. In all dimensions n we exhibit n bosonic functionally independent integrals of spinning particle motion, corresponding to explicit and hidden symmetries generated from the principal conformal Killing--Yano tensor. Moreover, we demonstrate that in 4-, 5-, 6-, and 7-dimensional black hole spacetimes such integrals are in involution, proving the bosonic part of the motion integrable. We conjecture that the same conclusion remains valid in all higher dimensions. Our result generalizes the result of Page et. al. [hep-th/0611083] on complete integrability of geodesic motion in these spacetimes.Comment: Version 2: revised version, added references. 5 pages, no figure