Robust online scale estimation in time series: A regression-free approach.

This paper presents variance extraction procedures for univariate time series. The volatility of a times series is monitored allowing for non-linearities, jumps and outliers in the level. The volatility is measured using the height of triangles formed by consecutive observations of the time series. This idea was proposed by Rousseeuw and Hubert (1996, Regression-free and robust estimation of scale for bivariate data, Computational Statistics and Data Analysis, 21, 67{85) in the bivariate setting. This paper extends their procedure to apply for online scale estimation in time series analysis. The statistical properties of the new methods are derived and nite sample properties are given. A nancial and a medical application illustrate the use of the procedures.Breakdown point; Inuence function; Online monitoring; Outliers; Robust scale estimation;

Residual-based localization and quantification of peaks in x-ray diffractograms

We consider data consisting of photon counts of diffracted x-ray radiation as a function of the angle of diffraction. The problem is to determine the positions, powers and shapes of the relevant peaks. An additional difficulty is that the power of the peaks is to be measured from a baseline which itself must be identified. Most methods of de-noising data of this kind do not explicitly take into account the modality of the final estimate. The residual-based procedure we propose uses the so-called taut string method, which minimizes the number of peaks subject to a tube constraint on the integrated data. The baseline is identified by combining the result of the taut string with an estimate of the first derivative of the baseline obtained using a weighted smoothing spline. Finally, each individual peak is expressed as the finite sum of kernels chosen from a parametric family.Comment: Published in at http://dx.doi.org/10.1214/08-AOAS181 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Methods and Algorithms for Robust Filtering

We discuss filtering procedures for robust extraction of a signal from noisy time series. Moving averages and running medians are standard methods for this, but they have shortcomings when large spikes (outliers) respectively trends occur. Modified trimmed means and linear median hybrid filters combine advantages of both approaches, but they do not completely overcome the difficulties. Improvements can be achieved by using robust regression methods, which work even in real time because of increased computational power and faster algorithms. Extending recent work we present filters for robust online signal extraction and discuss their merits for preserving trends, abrupt shifts and extremes and for the removal of spikes

Visualizing 1D Regression

Regression is the study of the conditional distribution of the response y given the predictors x. In a 1D regression, y is independent of x given a single linear combination βTx of the predictors. Special cases of 1D regression include multiple linear regression, binary regression and generalized linear models. If a good estimate ˆb of some non-zero multiple cβ of β can be constructed, then the 1D regression can be visualized with a scatterplot of ˆbTx versus y. A resistant method for estimating cβ is presented along with applications

Estimation in a Competing Risks Proportional Hazards Model Under Length-biased Sampling With Censoring

International audienceWhat population does the sample represent? The answer to this question is of crucial importance when estimating a survivor function in duration studies. As is well-known, in a stationary population, survival data obtained from a cross-sectional sample taken from the population at time $t_0$ represents not the target density $f(t)$ but its length-biased version proportional to $tf(t)$, for $t>0$. The problem of estimating survivor function from such length-biased samples becomes more complex, and interesting, in presence of competing risks and censoring. This paper lays out a sampling scheme related to a mixed Poisson process and develops nonparametric estimators of the survivor function of the target population assuming that the two independent competing risks have proportional hazards. Two cases are considered: with and without independent consoring before length biased sampling. In each case, the weak convergence of the process generated by the proposed estimator is proved. A well-known study of the duration in power for political leaders is used to illustrate our results. Finally, a simulation study is carried out in order to assess the finite sample behaviour of our estimators

Benzofuran-fused Phosphole: Synthesis, Electronic, and Electroluminescence Properties

International audienceA synthetic route to novel benzofuran-fused phosphole derivatives 3-5 is described. These compounds showed optical and electrochemical properties that differ from their benzothiophene analog. Preliminary results show that 4 can be used as an emitter in OLEDs, illustrating the potential of these new compounds for opto-electronic applications

A graphical vector autoregressive modelling approach to the analysis of electronic diary data

<p>Abstract</p> <p>Background</p> <p>In recent years, electronic diaries are increasingly used in medical research and practice to investigate patients' processes and fluctuations in symptoms over time. To model dynamic dependence structures and feedback mechanisms between symptom-relevant variables, a multivariate time series method has to be applied.</p> <p>Methods</p> <p>We propose to analyse the temporal interrelationships among the variables by a structural modelling approach based on graphical vector autoregressive (VAR) models. We give a comprehensive description of the underlying concepts and explain how the dependence structure can be recovered from electronic diary data by a search over suitable constrained (graphical) VAR models.</p> <p>Results</p> <p>The graphical VAR approach is applied to the electronic diary data of 35 obese patients with and without binge eating disorder (BED). The dynamic relationships for the two subgroups between eating behaviour, depression, anxiety and eating control are visualized in two path diagrams. Results show that the two subgroups of obese patients with and without BED are distinguishable by the temporal patterns which influence their respective eating behaviours.</p> <p>Conclusion</p> <p>The use of the graphical VAR approach for the analysis of electronic diary data leads to a deeper insight into patient's dynamics and dependence structures. An increasing use of this modelling approach could lead to a better understanding of complex psychological and physiological mechanisms in different areas of medical care and research.</p