Karen Schettlinger

Multivariate Real-Time Signal Extraction by a Robust Adaptive Regression Filter

We propose a new regression-based filter for extracting signals online from multivariate high frequency time series. It separates relevant signals of several variables from noise and (multivariate) outliers. Unlike parallel univariate filters, the new procedure takes into account the local covariance structure between the single time series components. It is based on high-breakdown estimates, which makes it robust against (patches of) outliers in one or several of the components as well as against outliers with respect to the multivariate covariance structure. Moreover, the trade-off problem between bias and variance for the optimal choice of the window width is approached by choosing the size of the window adaptively, depending on the current data situation. Furthermore, we present an advanced algorithm of our filtering procedure that includes the replacement of missing observations in real time. Thus, the new procedure can be applied in online-monitoring practice. Applications to physiological time series from intensive care show the practical effect of the proposed filtering technique.

Robust filters for intensive care monitoring: beyond the running median / Robuste Filter für intensivmedizinisches Monitoring: mehr als ein gleitender Median

Abstract Current alarm systems in intensive care units create a very high rate of false positive alarms because most of them simply compare physiological measurements to fixed thresholds. An improvement can be expected when the actual measurements are replaced by smoothed estimates of the underlying signal. However, classical filtering procedures are not appropriate for signal extraction, as standard assumptions, such as stationarity, do no hold here: the time series measured often show long periods without change, but also upward or downward trends, sudden shifts and numerous large measurement artefacts. Alternative approaches are needed to extract the relevant information from the data, i.e., the underlying signal of the monitored variables and the relevant patterns of change, such as abrupt shifts and trends. This article reviews recent research on filter-based online signal extraction methods designed for application in intensive care.

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.

Computing the least quartile difference estimator in the plane

A common problem in linear regression is that largely aberrant values can strongly influence the results. The least quartile difference (LQD) regression estimator is highly robust, since it can resist up to almost 50% largely deviant data values without becoming extremely biased. Additionally, it shows good behavior on Gaussian data – in contrast to many other robust regression methods. However, the LQD is not widely used yet due to the high computational effort needed when using common algorithms, e.g. the subset algorithm of Rousseeuw and Leroy. For computing the LQD estimator for n data points in the plane, we propose a randomized algorithm with expected running time O(n2 log2 n) and an approximation algorithm with a running time of roughly O(n2 log n). It can be expected that the practical relevance of the LQD estimator will strongly increase thereby.

Regression-based, regression-free and model-free approaches for robust online scale estimation

This paper compares methods for variability extraction from a univariate time series in real time. The online scale estimation is achieved by applying a robust scale functional to a moving time window. Scale estimators based on the residuals of a preceding regression step are compared with regressionfree and model-free techniques in a simulation study and in an application to a real time series. In the presence of level shifts or strong non-linear trends in the signal level, the model-free scale estimators perform especially well. However, the investigated regression-free and regression-based methods have higher breakdown points, they are applicable to data containing temporal correlations, and they are much more efficient.

Applying the Qn Estimator Online

Reliable automatic methods are needed for statistical online monitoring of noisy time series. Application of a robust scale estimator allows to use adaptive thresholds for the detection of outliers and level shifts. We propose a fast update algorithm for the Q n estimator and show by simulations that it leads to more powerful tests than other highly robust scale estimators.Reliable automatic methods are needed for statistical online monitoring of noisy time series. Application of a robust scale estimator allows to use adaptive thresholds for the detection of outliers and level shifts. We propose a fast update algorithm for the Q n estimator and show by simulations that it leads to more powerful tests than other highly robust scale estimators.

Robust and Adaptive Filtering of Multivariate Online-Monitoring Time Series

We propose a new regression-based filter for multivariate time series that separates signals from noise and outliers in real time. The new method merges the advantageous properties of two existent filtering procedures for online-monitoring time series. Our multivariate and robust procedure yields signal estimations at the right end point of a moving time window whose width is adapted to the current data situation. Since the proposed filter works in real time, it can be used, e.g., to lower the rate of false positive threshold alarms of intensive care online-monitoring systems.