Nonparametric maximum likelihood estimation of the structural mean of a sample of curves

A random sample of curves can be usually thought of as noisy realisations of a compound stochastic process X(t) = Z{W(t)}, where Z(t) produces random amplitude variation and W(t) produces random dynamic or phase variation. In most applications it is more important to estimate the so-called structural mean µ(t) = E{Z(t)} than the crosssectional mean E{X(t)}, but this estimation problem is difficult because the process Z(t) is not directly observable. In this paper we propose a nonparametric maximum likelihood estimator of µ(t). This estimator is shown to be {surd}n-consistent and asymptotically normal under the assumed model and robust to model misspecification. Simulations and a realdata example show that the proposed estimator is competitive with landmark registration, often considered the benchmark, and has the advantage of avoiding time-consuming and often infeasible individual landmark identificatio

1-(2,4,6-Trioxo-1,3-diazinan-5-yl­idene)thio­semicarbazide

The title mol­ecule, C5H5N5O3S, is approximately planar, with a maximum deviation from the mean plane through the non-H atoms of 0.182 (3) Å for the amine N atom. In the crystal, mol­ecules are connected via N—H⋯O and N—H⋯S inter­actions, building a three-dimensional hydrogen-bonded network. Additionally, a weak intra­molecular N—H⋯O hydrogen bond is observed

A Fast Algorithm for Robust Regression with Penalised Trimmed Squares

The presence of groups containing high leverage outliers makes linear regression a difficult problem due to the masking effect. The available high breakdown estimators based on Least Trimmed Squares often do not succeed in detecting masked high leverage outliers in finite samples. An alternative to the LTS estimator, called Penalised Trimmed Squares (PTS) estimator, was introduced by the authors in \cite{ZiouAv:05,ZiAvPi:07} and it appears to be less sensitive to the masking problem. This estimator is defined by a Quadratic Mixed Integer Programming (QMIP) problem, where in the objective function a penalty cost for each observation is included which serves as an upper bound on the residual error for any feasible regression line. Since the PTS does not require presetting the number of outliers to delete from the data set, it has better efficiency with respect to other estimators. However, due to the high computational complexity of the resulting QMIP problem, exact solutions for moderately large regression problems is infeasible. In this paper we further establish the theoretical properties of the PTS estimator, such as high breakdown and efficiency, and propose an approximate algorithm called Fast-PTS to compute the PTS estimator for large data sets efficiently. Extensive computational experiments on sets of benchmark instances with varying degrees of outlier contamination, indicate that the proposed algorithm performs well in identifying groups of high leverage outliers in reasonable computational time.Comment: 27 page

Non parametric estimation of the structural expectation of a stochastic increasing function

International audienceThis article introduces a non parametric warping model for functional data. When the outcome of an experiment is a sample of curves, data can be seen as realizations of a stochastic process, which takes into account the variations between the different observed curves. The aim of this work is to define a mean pattern which represents the main behaviour of the set of all the realizations. So, we define the structural expectation of the underlying stochastic function. Then, we provide empirical estimators of this structural expectation and of each individual warping function. Consistency and asymptotic normality for such estimators are proved

Análise interpretativa das dermatoses mais frequentes em Porto Alegre - Rio Grande do Sul - Brasil

Análise interpretativa das dermatoses mais frequentes em Porto Alegre - Rio Grande do Sul - Brasi

Bayesian Analysis of Curves Shape Variation Through Registration and Regression

This manuscript reviews the use of Bayesian hierarchical curve registration in Biostatistics and Bioinformatics.Several models allowing for unit-specific random time scales are discussed and applied to longitudinal dataarising in biomedicine, pharmacokinetics and time-course genomics. We consider representations of random functionals based on P-spline priors. Under this framework, straightforward posterior simulation strategies are outlined for inference.Beyond curve registration, we discuss jointregression modeling of both random effects and population level functional quantities. Finally, the use of mixture priors is discussed in the setting of differential expression analysis

Criteria for Evaluating Dimension-Reducing Components for Multivariate Data

Principal components are the benchmark for linear dimension reduction, but they are not always easy to interpret. For this reason, some alternatives have been proposed in recent years. These methods produce components that, unlike principal components, are correlated and/or have nonorthogonal loadings. This article shows that the criteria commonly used to evaluate principal components are not adequate for evaluating such alternatives, and proposes two new criteria that are more suitable for this purpose