Search results for "Uncertainty"
showing 10 items of 1010 documents
Tests and estimates of shape based on spatial signs and ranks
2009
Nonparametric procedures for testing and estimation of the shape matrix in the case of multivariate elliptic distribution are considered. Testing for sphericity is an important special case. The tests and estimates are based on the spatial sign and rank covariance matrices. The estimates based on the spatial sign covariance matrix and symmetrized spatial sign covariance matrix are Tyler's [A distribution-free M-estimator of multivariate scatter, Ann. Statist. 15 (1987), pp. 234–251] shape matrix and and Dümbgen's [On Tyler's M-functional of scatter in high dimension, Ann. Inst. Statist. Math. 50 (1998), pp. 471–491] shape matrix, respectively. The test based on the spatial sign covariance m…
On the relationship between the reversed hazard rate and elasticity
2012
Despite hazard and reversed hazard rates sharing a number of similar aspects, reversed hazard functions are far less frequently used. Understanding their meaning is not a simple task. The aim of this paper is to expand the usefulness of the reversed hazard function by relating it to other well-known concepts broadly used in economics: (linear or cumulative) rates of increase and elasticity. This will make it possible (i) to improve our understanding of the consequences of using a particular distribution and, in certain cases, (ii) to introduce our hypotheses and knowledge about the random process in a more meaningful and intuitive way, thus providing a means to achieving distributions that …
Building up adjusted indicators of students' evaluation of university courses using generalized item response models
2012
This article advances a proposal for building up adjusted composite indicators of the quality of university courses from students’ assessments. The flexible framework of Generalized Item Response Models is adopted here for controlling the sources of heterogeneity in the data structure that make evaluations across courses not directly comparable. Specifically, it allows us to: jointly model students’ ratings to the set of items which define the quality of university courses; explicitly consider the dimensionality of the items composing the evaluation form; evaluate and remove the effect of potential confounding factors which may affect students’ evaluation; model the intra-cluster variabilit…
Quantitative ergodicity for some switched dynamical systems
2012
International audience; We provide quantitative bounds for the long time behavior of a class of Piecewise Deterministic Markov Processes with state space Rd × E where E is a finite set. The continuous component evolves according to a smooth vector field that switches at the jump times of the discrete coordinate. The jump rates may depend on the whole position of the process. Under regularity assumptions on the jump rates and stability conditions for the vector fields we provide explicit exponential upper bounds for the convergence to equilibrium in terms of Wasserstein distances. As an example, we obtain convergence results for a stochastic version of the Morris-Lecar model of neurobiology.
Gossip: The Architecture of SpreadPlots
2003
A spreadplot is a visualization that simultaneously shows several different views of a dataset or model. The individual views can be dynamic, can support high-interaction direct manipulation, and can be algebraically linked with each other, possibly via an underlying statistical model. Thus, when a data analyst changes the information shown in one view of a statistical model, the changes can be processed by the model and instantly represented in the other views. Spreadplots simplify the analyst's task when many different plots are relevant to the analysis at hand, as is the case in regression analysis, where there are many plots that can be used for model building and diagnosis. On the othe…
Bayesian Design of “Successful” Replications
2002
Replication of experiments is commonin applied research. However, systematic studies of the goals and motivations of a “replication” are rare. As a consequence, there does not seem to be a precise notion of what a “success” when replicating means. This article discusses some of the possible goals for replication; this leads to different (but precise) notions of “success” when replicating. Bayesian hierarchical models allow for a flexible and explicit incorporation of the assumed relationship among the experiments. Bayesian predictive distributions are a natural tool to compute the probability of the replication being successful, and hence to design the replication so that the probability of…
Portfolio optimisation with strictly positive transaction costs and impulse control
1998
One crucial assumption in modern portfolio theory of continuous-time models is the no transaction cost assumption. This assumption normally leads to trading strategies with infinite variation. However, following such a strategy in the presence of transaction costs will lead to immediate ruin. We present an impulse control approach where the investor can change his portfolio only finitely often in finite time intervals. Further, we consider transaction costs including a fixed and a proportional cost component. For the solution of the resulting control problems we present a formal optimal stopping approach and an approach using quasi-variational inequalities. As an application we derive a non…
A Bayesian SIRS model for the analysis of respiratory syncytial virus in the region of Valencia, Spain
2014
We present a Bayesian stochastic susceptible-infected-recovered-susceptible (SIRS) model in discrete time to understand respiratory syncytial virus dynamics in the region of Valencia, Spain. A SIRS model based on ordinary differential equations has also been proposed to describe RSV dynamics in the region of Valencia. However, this continuous-time deterministic model is not suitable when the initial number of infected individuals is small. Stochastic epidemic models based on a probability of disease transmission provide a more natural description of the spread of infectious diseases. In addition, by allowing the transmission rate to vary stochastically over time, the proposed model provides…
Eleccion de variables en regresion lineal un problema de decision
1986
A general structure for the problem of selection of variables in regression is proposed using the decision theory framework. In particular, some results for the choice of the best linear normal homocedastic model are obtained when the main purpose is either to specify the predictive distribution over the response variable or to obtain a point estimate of it. A comparison of our results with the most widespread classical ones is presented
Asymptotic efficiency of the calibration estimator in a high-dimensional data setting
2022
Abstract In a finite population sampling survey, auxiliary information is commonly used to improve the Horvitz-Thompson estimators and calibration has been extensively used by national statistical agencies over the last decades for that purpose. This method enables to make estimators consistent with known totals of auxiliary variables and to reduce variance if the calibration variables are explanatory for the variable of interest. Nowadays, it is not unusual anymore to have high-dimensional auxiliary data sets and adding too much additional calibration variables may increase the variance of calibration estimators. We study in this paper the asymptotic efficiency of the calibration estimator…