Search results for " Linear"

Quantum graphs with mixed dynamics: the transport/diffusion case

2013

We introduce a class of partial differential equations on metric graphs associated with mixed evolution: on some edges we consider diffusion processes, on other ones transport phenomena. This yields a system of equations with possibly nonlocal couplings at the boundary. We provide sufficient conditions for these to be governed by a contractive semigroup on a Hilbert space naturally associated with the system. We show that our setting is also adequate to discuss specific systems of diffusion equations with boundary delays.

Varying-time random effects models for longitudinal data: unmixing and temporal interpolation of remote-sensing data

2008

Remote sensing is a helpful tool for crop monitoring or vegetation-growth estimation at a country or regional scale. However, satellite images generally have to cope with a compromise between the time frequency of observations and their resolution (i.e. pixel size). When concerned with high temporal resolution, we have to work with information on the basis of kilometric pixels, named mixed pixels, that represent aggregated responses of multiple land cover. Disaggreggation or unmixing is then necessary to downscale from the square kilometer to the local dynamic of each theme (crop, wood, meadows, etc.). Assuming the land use is known, that is to say the proportion of each theme within each m…

Simulation in the Simple Linear Regression Model

2002

Summary This article presents an activity which simulates the linear regression model in order to verify the probabilistic behaviour of the resulting least-squares statistics in practice.

Linear and ellipsoidal restrictions in linear regression

1991

The problem of combining linear and ellipsoidal restrictions in linear regression is investigated. Necessary and sufficient conditions for compactness of the restriction set are proved assuring the existence of a minimax estimator. When the restriction set is not compact a minimax estimator may still exist for special loss functions arid regression designs

Varying-coefficient functional linear regression models

2008

This article considers a generalization of the functional linear regression in which an additional real variable influences smoothly the functional coefficient. We thus define a varying-coefficient regression model for functional data. We propose two estimators based, respectively, on conditional functional principal regression and on local penalized regression splines and prove their pointwise consistency. We check, with the prediction one day ahead of ozone concentration in the city of Toulouse, the ability of such nonlinear functional approaches to produce competitive estimations.

Estimating regression models with unknown break-points.

2003

This paper deals with fitting piecewise terms in regression models where one or more break-points are true parameters of the model. For estimation, a simple linearization technique is called for, taking advantage of the linear formulation of the problem. As a result, the method is suitable for any regression model with linear predictor and so current software can be used; threshold modelling as function of explanatory variables is also allowed. Differences between the other procedures available are shown and relative merits discussed. Simulations and two examples are presented to illustrate the method.

Testing with a nuisance parameter present only under the alternative: a score-based approach with application to segmented modelling

2016

ABSTRACTWe introduce a score-type statistic to test for a non-zero regression coefficient when the relevant term involves a nuisance parameter present only under the alternative. Despite the non-regularity and complexity of the problem and unlike the previous approaches, the proposed test statistic does not require the nuisance to be estimated. It is simple to implement by relying on the conventional distributions, such as Normal or t, and it justified in the setting of probabilistic coherence. We focus on testing for the existence of a breakpoint in segmented regression, and illustrate the methodology with an analysis on data of DNA copy number aberrations and gene expression profiles from…

Escape Times in Fluctuating Metastable Potential and Acceleration of Diffusion in Periodic Fluctuating Potentials

2004

The problems of escape from metastable state in randomly flipping potential and of diffusion in fast fluctuating periodic potentials are considered. For the overdamped Brownian particle moving in a piecewise linear dichotomously fluctuating metastable potential we obtain the mean first-passage time (MFPT) as a function of the potential parameters, the noise intensity and the mean rate of switchings of the dichotomous noise. We find noise enhanced stability (NES) phenomenon in the system investigated and the parameter region of the fluctuating potential where the effect can be observed. For the diffusion of the overdamped Brownian particle in a fast fluctuating symmetric periodic potential w…

Reference Posterior Distributions for Bayesian Inference

1979

Electricity consumption prediction with functional linear regression using spline estimators

2010

A functional linear regression model linking observations of a functional response variable with measurements of an explanatory functional variable is considered. This model serves to analyse a real data set describing electricity consumption in Sardinia. The interest lies in predicting either oncoming weekends’ or oncoming weekdays’ consumption, provided actual weekdays’ consumption is known. A B-spline estimator of the functional parameter is used. Selected computational issues are addressed as well.