Hyper-Fit: Fitting Linear Models to Multidimensional Data with Multivariate Gaussian Uncertainties

Parametric Piecewise Linear Models with Good Fit to the Data

This paper addresses the problem of piecewise linear approximation of point sets without any constraints on the order of data points or the number of model components (line segments). The point sets can be obtained as edge pixels in digital images or from a laser range scanner mounted on a moving robot. We point out two problems with the maximum likelihood estimate (MLE) that present serious dr...

Gaussian Scale Mixture Models for Robust Linear Multivariate Regression with Missing Data

Goodness-of-fit Tests for high-dimensional Gaussian linear models

Let (Y, (Xi)1≤i≤p) be a real zero mean Gaussian vector and V be a subset of {1, . . . , p}. Suppose we are given n i.i.d. replications of this vector. We propose a new test for testing that Y is independent of (Xi)i∈{1,...p}\V conditionally to (Xi)i∈V against the general alternative that it is not. This procedure does not depend on any prior information on the covariance of X or the variance of...

Data Fitting Problems with Bounded Uncertainties in the Data

Joint segmentation of multivariate Gaussian processes using mixed linear models

The joint segmentation of multiple series is considered. A mixed linear model is used to account for both covariates and correlations between signals. An estimation algorithm based on EM which involves a new dynamic programming strategy for the segmentation step is proposed. The computational efficiency of this procedure is shown and its performance is assessed through simulation experiments. A...