Phantom distribution functions for some stationary sequences

The notion of a phantom distribution function (phdf) was introduced by O'Brien (1987). We show that the existence of a phdf is a quite common phenomenon for stationary weakly dependent sequences. It is proved that any $\alpha$-mixing stationary sequence with continuous marginals admits a continuous phdf. Sufficient conditions are given for stationary sequences exhibiting weak dependence, what allows the use of attractive models beyond mixing. The case of discontinuous marginals is also discussed for $\alpha$-mixing. Special attention is paid to examples of processes which admit a continuous phantom distribution function while their extremal index is zero. We show that Asmussen (1998) and Roberts et al. (2006) provide natural examples of such processes. We also construct a non-ergodic stationary process of this type

How many candidates are needed to make elections hard to manipulate?

In multiagent settings where the agents have different preferences, preference aggregation is a central issue. Voting is a general method for preference aggregation, but seminal results have shown that all general voting protocols are manipulable. One could try to avoid manipulation by using voting protocols where determining a beneficial manipulation is hard computationally. The complexity of manipulating realistic elections where the number of candidates is a small constant was recently studied (Conitzer 2002), but the emphasis was on the question of whether or not a protocol becomes hard to manipulate for some constant number of candidates. That work, in many cases, left open the question: How many candidates are needed to make elections hard to manipulate? This is a crucial question when comparing the relative manipulability of different voting protocols. In this paper we answer that question for the voting protocols of the earlier study: plurality, Borda, STV, Copeland, maximin, regular cup, and randomized cup. We also answer that question for two voting protocols for which no results on the complexity of manipulation have been derived before: veto and plurality with runoff. It turns out that the voting protocols under study become hard to manipulate at 3 candidates, 4 candidates, 7 candidates, or never

Boolean Hedonic Games

We study hedonic games with dichotomous preferences. Hedonic games are cooperative games in which players desire to form coalitions, but only care about the makeup of the coalitions of which they are members; they are indifferent about the makeup of other coalitions. The assumption of dichotomous preferences means that, additionally, each player's preference relation partitions the set of coalitions of which that player is a member into just two equivalence classes: satisfactory and unsatisfactory. A player is indifferent between satisfactory coalitions, and is indifferent between unsatisfactory coalitions, but strictly prefers any satisfactory coalition over any unsatisfactory coalition. We develop a succinct representation for such games, in which each player's preference relation is represented by a propositional formula. We show how solution concepts for hedonic games with dichotomous preferences are characterised by propositional formulas.Comment: This paper was orally presented at the Eleventh Conference on Logic and the Foundations of Game and Decision Theory (LOFT 2014) in Bergen, Norway, July 27-30, 201

A functional central limit theorem for interacting particle systems on transitive graphs

A finite range interacting particle system on a transitive graph is considered. Assuming that the dynamics and the initial measure are invariant, the normalized empirical distribution process converges in distribution to a centered diffusion process. As an application, a central limit theorem for certain hitting times, interpreted as failure times of a coherent system in reliability, is derived.Comment: 35 page

Dependent Lindeberg central limit theorem and some applications

In this paper, a very useful lemma (in two versions) is proved: it simplifies notably the essential step to establish a Lindeberg central limit theorem for dependent processes. Then, applying this lemma to weakly dependent processes introduced in Doukhan and Louhichi (1999), a new central limit theorem is obtained for sample mean or kernel density estimator. Moreover, by using the subsampling, extensions under weaker assumptions of these central limit theorems are provided. All the usual causal or non causal time series: Gaussian, associated, linear, ARCH($\infty$), bilinear, Volterra processes,$...$, enter this frame

The Complexities of Developing a Personal Code of Ethics for Learning Analytics Practitioners: Implications for Institutions and the Field

In this paper we explore the potential role, value and utility of a personal code of ethics (COE) for learning analytics practitioners, and in particular we consider whether such a COE might usefully mediate individual actions and choices in relation to a more abstract institutional COE. While several institutional COEs now exist, little attention has been paid to detailing the ethical responsibilities of individual practitioners. To investigate the problems associated with developing and implementing a personal COE, we drafted an LA Practitioner COE based on other professional codes, and invited feedback from a range of learning analytics stakeholders and practitioners: ethicists, students, researchers and technology executives. Three main themes emerged from their reflections: 1. A need to balance real world demands with abstract principles, 2. The limits to individual accountability within the learning analytics space, and 3. The continuing value of debate around an aspirational code of ethics within the field of learning analytics

Spectral variations of the X-ray binary pulsar LMC X-4 during its long period intensity variation and a comparison with Her X-1

We present spectral variations of the binary X-ray pulsar LMC X-4 using the RXTE/PCA observations at different phases of its 30.5 day long super-orbital period. Only out of eclipse data were used for this study. During the high state of the super-orbital period of LMC X-4, the spectrum is well described by a high energy cut-off power-law with a photon index in the range of 0.7-1.0 and an iron emission line. In the low state, the spectrum is found to be flatter with power-law photon index in the range 0.5-0.7. A direct correlation is detected between the continuum flux in 7-25 keV energy band and the iron emission line flux. The equivalent width of the iron emission line is found to be highly variable during low intensity state, whereas it remains almost constant during the high intensity state of the super-orbital period. It is observed that the spectral variations in LMC X-4 are similar to those of Her X-1 (using RXTE/PCA data). These results suggest that the geometry of the region where the iron line is produced and its visibility with respect to the phase of the super-orbital period is similar in LMC X-4 and Her X-1. A remarkable difference between these two systems is a highly variable absorption column density with phase of the super-orbital period that is observed in Her X-1 but not in LMC X-4.Comment: 7 pages, 5 figures, Accepted for publication in Astronomy and Astrophysic

Evaluation for moments of a ratio with application to regression estimation

Many problems involve ratios in probability or in statistical applications. We aim at approximating the moments of such ratios under specific assumptions. Using ideas from Collomb (1977) we propose sharper bounds for the moments of randomly weighted sums which also may appear as a ratio of two random variables. Suitable applications are given in more detail here in the fields of functional estimation, in finance and for censored data analysis. Several weak dependence dependence situations are considered