Search results for "STATISTICS & PROBABILITY"
showing 10 items of 436 documents
Influence Functions and Efficiencies of k-Step Hettmansperger–Randles Estimators for Multivariate Location and Regression
2016
In Hettmansperger and Randles (Biometrika 89:851–860, 2002) spatial sign vectors were used to derive simultaneous estimators of multivariate location and shape. Oja (Multivariate nonparametric methods with R. Springer, New York, 2010) proposed a similar approach for the multivariate linear regression case. These estimators are highly robust and have under general assumptions a joint limiting multinormal distribution. The estimates are easy to compute using fixed-point algorithms. There are however no exact proofs for the convergence of these algorithms. The existence and uniqueness of the solutions also still remain unproven although we believe that they hold under general conditions. To ci…
Modelling systemic price cojumps with Hawkes factor models
2015
Instabilities in the price dynamics of a large number of financial assets are a clear sign of systemic events. By investigating a set of 20 high cap stocks traded at the Italian Stock Exchange, we find that there is a large number of high frequency cojumps. We show that the dynamics of these jumps is described neither by a multivariate Poisson nor by a multivariate Hawkes model. We introduce a Hawkes one factor model which is able to capture simultaneously the time clustering of jumps and the high synchronization of jumps across assets.
Testing Equality of Multiple Power Spectral Density Matrices
2018
This paper studies the existence of optimal invariant detectors for determining whether P multivariate processes have the same power spectral density. This problem finds application in multiple fields, including physical layer security and cognitive radio. For Gaussian observations, we prove that the optimal invariant detector, i.e., the uniformly most powerful invariant test, does not exist. Additionally, we consider the challenging case of close hypotheses, where we study the existence of the locally most powerful invariant test (LMPIT). The LMPIT is obtained in the closed form only for univariate signals. In the multivariate case, it is shown that the LMPIT does not exist. However, the c…
Locally optimal invariant detector for testing equality of two power spectral densities
2018
This work addresses the problem of determining whether two multivariate random time series have the same power spectral density (PSD), which has applications, for instance, in physical-layer security and cognitive radio. Remarkably, existing detectors for this problem do not usually provide any kind of optimality. Thus, we study here the existence under the Gaussian assumption of optimal invariant detectors for this problem, proving that the uniformly most powerful invariant test (UMPIT) does not exist. Thus, focusing on close hypotheses, we show that the locally most powerful invariant test (LMPIT) only exists for univariate time series. In the multivariate case, we prove that the LMPIT do…
A quantitative analysis of Educational Data through the Comparison between Hierarchical and Not-Hierarchical Clustering
2017
Many research papers have studied the problem of taking a set of data and separating it into subgroups through the methods of Cluster Analysis. However, the variables and parameters involved in Cluster Analysis have not always been outlined and criticized, especially in the field of Science Education. Moreover, in the field of Science Education, a comparison between two different Clustering methods is not discussed in the literature. Conceptions of students about modeling in physic are investigated by using an open-ended questionnaire. The questionnaire is analyzed through Clustering methods. The clustering results obtained by using the two methods are compared and show a good coherence bet…
Multi-state relative survival modelling of colorectal cancer progression and mortality.
2015
Abstract Accurate identification of factors associated with progression of colorectal cancer remains a challenge. In particular, it is unclear which statistical methods are most suitable to separate the effects of putative prognostic factors on cancer progression vs cancer-specific and other cause mortality. To address these challenges, we analyzed 10 year follow-up data for patients who underwent curative surgery for colorectal cancer in 1985–2000. Separate analyses were performed in two French cancer registries. Results of three multivariable models were compared: Cox model with recurrence as a time-dependent variable, and two multi-state models, which separated prognostic factor effects …
M/M/1 queue in two alternating environments and its heavy traffic approximation
2018
We investigate an M/M/1 queue operating in two switching environments, where the switch is governed by a two-state time-homogeneous Markov chain. This model allows to describe a system that is subject to regular operating phases alternating with anomalous working phases or random repairing periods. We first obtain the steady-state distribution of the process in terms of a generalized mixture of two geometric distributions. In the special case when only one kind of switch is allowed, we analyze the transient distribution, and investigate the busy period problem. The analysis is also performed by means of a suitable heavy-traffic approximation which leads to a continuous random process. Its d…
Patterns of poverty among elderly Americans: a Latent Class Markov Model
2017
ABSTRACTThis article studies poverty persistence and the role of social security programmes on poverty among elderly in the US. We use a Latent Markov model to disentangle unobserved heterogeneity and state dependence. Because of its dynamic nature, unobserved heterogeneity is modelled to vary over time. This allows to capture different latent states of poverty that change over time. Result indicates the existence of three unobserved types evolving over time according to their propensity to be poor. Moreover, a strong persistence in poverty especially for women, individuals living alone and ethnic minorities is found. Finally, the estimates indicate that giving social assistance tends to re…
Numerical Solution of Fuzzy Differential Equations with Z-numbers using Fuzzy Sumudu Transforms
2018
The uncertain nonlinear systems can be modeled with fuzzy differential equations (FDEs) and the solutions of these equations are applied to analyze many engineering problems. However, it is very difficult to obtain solutions of FDEs. In this paper, the solutions of FDEs are approximated by utilizing the fuzzy Sumudu transform (FST) method. Here, the uncertainties are in the sense of Z-numbers. Important theorems are laid down to illustrate the properties of FST. The theoretical analysis and simulation results show that this new technique is effective to estimate the solutions of FDEs.
Bifurcation of traveling waves in a Keller–Segel type free boundary model of cell motility
2018
We study a two-dimensional free boundary problem that models motility of eukaryotic cells on substrates. This problem consists of an elliptic equation describing the flow of cytoskeleton gel coupled with a convection-diffusion PDE for the density of myosin motors. The two key properties of this problem are (i) presence of the cross diffusion as in the classical Keller-Segel problem in chemotaxis and (ii) nonlinear nonlocal free boundary condition that involves curvature of the boundary. We establish the bifurcation of the traveling waves from a family of radially symmetric steady states. The traveling waves describe persistent motion without external cues or stimuli which is a signature of …