Si-GARCH: Construction and validation of a new method for the detection of breaking points in models

In this article, we define a new method (Si-GARCH) for signal segmentation based on a class of models coming from econometrics. We make use of these models not to perform prediction but to characterize portions of signals. This enables us to compare these portions in order to determine if there is a change in the signal’s dynamics and to define breaking points with an aim of segmenting it according to its dynamics. We, then, expand these models by defining a new coefficient to improve their accuracy. The Si-GARCH method was tested on several thousands of hours of biomedical signals coming from intensive care units.     

Robust analysis of variance for a randomized block design

In this paper we study the asymptotic theory of M-estimates and their associated tests for a one-factor experiment in a randomized block design. In this case one natural asymptotic theory corresponds to leaving the number of treatments fixed and letting the number of blocks tend to infinity. The classic asymptotic theory of M-estimates does not apply here, because the number of parameters and the number of observations are of the same order. In this paper we prove the consistency and asymptotic normality of the estimators of the treatment effects. It turns out that the asymptotic covariance matrix of the treatment effects estimators differs from the one derived from the classic theory of M-estimates for the linear model with a fixed number of parameters. We also study a test for treatment effects derived from M-estimates and we compare by Monte Carlo simulation the efficiency of this test with respect to the F-test, the Friedman test and the test based on aligned ranks.     

On the generalization of the hazard rate twisting-based simulation approach

Estimating the probability that a sum of random variables (RVs) exceeds a given threshold is a well-known challenging problem. A naive Monte Carlo simulation is the standard technique for the estimation of this type of probability. However, this approach is computationally expensive, especially when dealing with rare events. An alternative approach is represented by the use of variance reduction techniques, known for their efficiency in requiring less computations for achieving the same accuracy requirement. Most of these methods have thus far been proposed to deal with specific settings under which the RVs belong to particular classes of distributions. In this paper, we propose a generalization of the well-known hazard rate twisting Importance Sampling-based approach that presents the advantage of being logarithmic efficient for arbitrary sums of RVs. The wide scope of applicability of the proposed method is mainly due to our particular way of selecting the twisting parameter. It is worth observing that this interesting feature is rarely satisfied by variance reduction algorithms whose performances were only proven under some restrictive assumptions. It comes along with a good efficiency, illustrated by some selected simulation results comparing the performance of the proposed method with some existing techniques.     

Explicit expressions for gamma spacings and their moments

This work is concerned with the distributions of spacings from a two-parameter gamma distribution, when the shape parameter is a positive integer (or Erlang Distribution). We express the probability density functions of spacings and their moments in closed forms that are easy to implement using computer algebra systems like Mathematica.     

再论经济法的基础

经济法有其社会、经济和政治基础。这种基础集中表现为各种思想主张和制度安排。就其社会基础而言核心是个人自由与社会秩序,就其经济基础而言核心是市场调节与国家干预,就其政治基础而言核心是契约自由与人权保障,而上述三者又可进一步归结为自由竞争与秩序调控。在这些基础上形成一种特定的社会关系,即市场竞争关系和宏观调控关系,它由经济法调整,进而构成经济法的基础。