Fried, Roland Robust filtering of time series with trends. (English) Zbl 1065.62162 J. Nonparametric Stat. 16, No. 3-4, 313-328 (2004). Summary: 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 of 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. Cited in 9 Documents MSC: 62M20 Inference from stochastic processes and prediction 62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH) 62P10 Applications of statistics to biology and medical sciences; meta analysis 62F35 Robustness and adaptive procedures (parametric inference) 65C60 Computational problems in statistics (MSC2010) Keywords:Online Monitoring; Signal Extraction; Level Shift; Trend; Outlier; Bias Curve PDFBibTeX XMLCite \textit{R. Fried}, J. Nonparametric Stat. 16, No. 3--4, 313--328 (2004; Zbl 1065.62162) Full Text: DOI Link References: [1] Davies PL, J. Statist. Plann. and Inference 122 pp 65– · Zbl 1040.62099 [2] Tukey JW, Exploratory Data Analysis, Addison-Wesley (1977) [3] Fried R, Proceedings in Computational Statistics COMPSTAT 2002, Physica-Verlag pp pp. 367–372– (2002) [4] Davies PL, Ann. Statist. 21 pp 1843– (1993) · Zbl 0797.62026 [5] Rousseeuw PJ, J. Amer. Statist. Assoc. 88 pp 1273– (1993) [6] Fan J, Scand. J. Statist. 21 pp 433– (1994) [7] Rue H, J. Nonparametr. Statist. 14 pp 155– (2002) · Zbl 1011.62044 [8] Gather U, Estadistica 53 pp 259– (2001) [9] Smith AFM, Biometrics 39 pp 867– (1983) · Zbl 0556.62079 [10] Hampel FR, Bulletin of the Int. Statist. Inst. 46 pp 375– (1975) [11] Rousseeuw PJ, J. Amer. Statist. Assoc. 79 pp 871– (1984) [12] Siegel AF, Biometrika 68 pp 242– (1982) · Zbl 0483.62026 [13] Bernholt T, Information Processing Letters 88 pp 111– · Zbl 1178.68607 [14] Hettmansperger TP, Amer. Statist. 46 pp 79– (1992) [15] Gather U, Proceedings of the Fourth International Conference on Mathematical Statistics PROBASTAT 2002, Tatra Mountain Mathematical Publications 26 pp 87– [16] Grübel R, Ann. Statist. 16 pp 619– (1988) · Zbl 0664.62040 [17] Rousseeuw PJ, Statistica Neerlandica 42 pp 103– (1988) · Zbl 0652.62032 [18] Croux C, Computational Statistics 1 pp pp. 411–428– (1992) [19] Martin RD, Ann. Statist. 21 pp 991– (1993) · Zbl 0787.62038 [20] Basseville M, Detection of Abrupt Changes – Theory and Application, Prentice-Hall (1993) [21] Imhoff M, Intensive Care Medicine 24 pp 1305– (1998) [22] Berrendero JR, Statist. Probab. Lett. 44 pp 63– (1999) · Zbl 0940.62029 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.