Search

In many applications the standard deviation of the observations needs to be estimated, e.g., for standardization. In the presence of outliers and jumps in the mean suitable estimation procedures are required, since ordinary scale estimators are biased in such situations. We propose a modification of the median absolute deviation (MAD) based on segregating the data into many non-overlapping blocks, which performs well in the outlier and change-point scenario, as can be seen in a simulation study. Theoretical results, such as strong consistency and asymptotic normality, are shown. Moreover, suggestions on the choice of the block size are given. We compare the performance of the proposed estimation procedure with that of other robust estimation techniques. [ABSTRACT FROM AUTHOR]

We study residual control charts for the detection of sudden changes in time series with an underlying time-varying trend. Our control charts compare the most recent observations to their direct predecessors by applying two-sample tests in a moving time window to one-step-ahead prediction errors obtained from a local linear regression. Global model assumptions, a fixed target value, or large sets of historical in-control data are unnecessary therefore. Disturbing in-control structures, like short outlier patches or minor fluctuations, are resisted by using robust methods. Our simulation results indicate that a control chart based on the two-sample Hodges-Lehmann estimator in combination with repeated-median regression possesses an approximately distribution-free in-control average run length, good robustness against outliers, and a desirable detection quality. [ABSTRACT FROM AUTHOR]

We propose and investigate robust control charts for the detection of sudden shifts in sequences of very noisy observations with a naturally slowly varying mean. They sequentially apply local two-sample tests for the location problem. Thus, no previous knowledge about the in-control behaviour is necessary. We identify critical values for the tests to achieve a desired in-control average run length () with extensive simulations. Control charts based on non-parametric tests or a randomization principle provide a satisfactory run length behaviour for different error distributions. They possess a nearly distribution-freeand are fast in detecting present signal jumps in a time series. In our simulations and exemplary real-world applications from biosignal analysis, a test based on the two-sample Hodges–Lehmann estimator leads to very promising results regarding distribution independence, robustness and detection speed. [ABSTRACT FROM PUBLISHER]

We introduce a new way to construct variables for classification in a setting of astronomy. The newly constructed variables complement the currently used Hillas parameters and are specifically designed to improve the classification. They are based on fitting elliptic or skewed bivariate distributions to images gathered by imaging atmospheric Cherenkov telescopes and evaluating the distance between the observed and the fitted distribution. As distance measures we use the Chi-square distance, the Kullback–Leibler divergence and the Hellinger distance. The new variables lead to an improved classification in terms of misclassification errors. [ABSTRACT FROM AUTHOR]

We study different approaches for modelling intervention effects in time series of counts, focusing on the so-called integer-valued GARCH models. A previous study treated a model where an intervention affects the non-observable underlying mean process at the time point of its occurrence and additionally the whole process thereafter via its dynamics. As an alternative, we consider a model where an intervention directly affects the observation at its occurrence, but not the underlying mean, and then also enters the dynamics of the process. While the former definition describes an internal change of the system, the latter can be understood as an external effect on the observations due to e.g. immigration. For our alternative model we develop conditional likelihood estimation and, based on this, tests and detection procedures for intervention effects. Both models are compared analytically and using simulated and real data examples. We study the effect of model misspecification and computational issues. [ABSTRACT FROM PUBLISHER]

Prediction of demand for professional sports is increasingly drawing the attention of economists. We apply linear mixed models for modeling attendance figures at Spanish professional football. We investigate economic variables, such as the price of the tickets or the size of the market, and sporting variables, such as the quality of a team or the level of competition within the league, as potential predictors of attendance. It turns out that a model with temporally correlated random team effects provides good forecasts of attendance at a time horizon of two seasons. Results from this model agree with economic theory. [ABSTRACT FROM AUTHOR]

We propose weighted repeated median filters and smoothers for robust nonparametric regression in general and for robust online signal extraction from time series in particular. The new methods allow us to remove outlying sequences and to preserve discontinuities (shifts) in the underlying regression function (the signal) in the presence of local linear trends. Suitable weighting of the observations according to their distances in the design space reduces the bias arising from nonlinearities and improves the efficiency using larger bandwidths, while still distinguishing long-term shifts from outlier sequences. Other localized robust regression techniques like S, M, and MM estimators as well as weighted L1 regression, are examined for comparison. [ABSTRACT FROM AUTHOR]

We discuss the approximation of the mean of autocorrelated data under contaminations of different types. Many robust location estimators have been investigated carefully for independent data, but their properties have not been studied in detail under dependencies. We pay attention to estimators based on subranges like minimum volume ellipsoid and minimum covariance determinant estimators, mid-ranges and trimmed means, of which the sample mean and median are special cases, and also include the Hodges–Lehmann and the Bickel–Hodges estimators. Our interest is in small to moderate sample sizes. [ABSTRACT FROM AUTHOR]

We develop and test a robust procedure for extracting an underlying signal in form of a time-varying trend from very noisy time series. The application we have in mind is online monitoring data measured in intensive care, where we find periods of relative constancy, slow monotonic trends, level shifts and many measurement artifacts. A method is needed which allows a fast and reliable denoising of the data and which distinguishes artifacts from clinically relevant changes in the patient's condition. We use robust regression functionals for local approximation of the trend in a moving time window. For further improving the robustness of the procedure, we investigate online outlier replacement by e.g. trimming or winsorization based on robust scale estimators. The performance of several versions of the procedure is compared in important data situations and applications to real and simulated data are given. [ABSTRACT FROM AUTHOR]

Examines the linear mixed models as a tool in analyzing longitudinal data. Capability of the recursive linear models in allowing interactions between the endogenous variables in multivariate regression; Occurrence of difficulties in linear models due to parameter restrictions; Derivation of analytical distributions of two-stage generalized-least-squares estimators for shared coefficients.