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Statistical Surveillance. Optimality and Methods

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  • Marianne Frisén

Abstract

Different criteria of optimality are used in different subcultures of statistical surveillance. One aim with this review is to bridge the gap between the different areas. The shortcomings of some criteria of optimality are demonstrated by their implications. Some commonly used methods are examined in detail, with respect to optimality. The examination is made for a standard situation in order to focus on the inferential principles. A uniform presentation of methods, by expressions of likelihood ratios, facilitates the comparisons between methods. The correspondences between criteria of optimality and methods are examined. The situations and parameter values for which some commonly used methods have optimality properties are thus determined. A linear approximation of the full likelihood ratio method, which satisfies several criteria of optimality, is presented. This linear approximation is used to examine when linear methods are approximately optimal. Methods for complicated situations are reviewed with respect to optimality and robustness. Des différents critères d'optimalité sont utilisés dans différentes subcultures de la surveillance statistique. Un des objectifs de cette étude est celui d'établir un rapprochement entre les différentes disciplines. Les faults de quelques uns des critères d'optimalité sont montrés par leurs implications. Quelques méthodes fréquemment utilisées sont examinées en détail quant à leur optimalité. Cet analyse est fait pour une situation standard, se concentrant sur les principes d'inférence. Une présentation uniforme des méthodes, par expressions de rapports de vraisemblance, facilite la comparaison entre les méthodes. On examine les correspondances entre les critères d'optimalité et les méthodes. On présente une approximation linéaire de la méthode du rapport de vraisemblance totale, qui satisfait plusieurs critères de optimalité. Cette approximation linéaire est utilisée pour examiner quand les méthodes linéaires sont approximativent optimales. Des méthodes pour des situations compliquées sont étudiées quant à leur optimalité est robustesse.

Suggested Citation

  • Marianne Frisén, 2003. "Statistical Surveillance. Optimality and Methods," International Statistical Review, International Statistical Institute, vol. 71(2), pages 403-434, August.
    • Handle: RePEc:bla:istatr:v:71:y:2003:i:2:p:403-434
    DOI: 10.1111/j.1751-5823.2003.tb00205.x
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    Cited by:

    1. Taras Lazariv & Wolfgang Schmid, 2019. "Surveillance of non-stationary processes," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 103(3), pages 305-331, September.
    2. Bock, David, 2007. "Evaluations of likelihood based surveillance of volatility," Research Reports 2007:9, University of Gothenburg, Statistical Research Unit, School of Business, Economics and Law.
    3. Marianne Frisén, 2014. "Spatial outbreak detection based on inference principles for multivariate surveillance," IISE Transactions, Taylor & Francis Journals, vol. 46(8), pages 759-769, August.
    4. Vasyl Golosnoy, 2018. "Sequential monitoring of portfolio betas," Statistical Papers, Springer, vol. 59(2), pages 663-684, June.
    5. Pettersson, Kjell, 2008. "On curve estimation under order restrictions," Research Reports 2007:15, University of Gothenburg, Statistical Research Unit, School of Business, Economics and Law.
    6. Schiöler, Linus & Frisén, Marianne, 2008. "On statistical surveillance of the performance of fund managers," Research Reports 2008:4, University of Gothenburg, Statistical Research Unit, School of Business, Economics and Law.
    7. Frisén, Marianne & Andersson, Eva & Schiöler, Linus, 2009. "Sufficient reduction in multivariate surveillance," Research Reports 2009:2, University of Gothenburg, Statistical Research Unit, School of Business, Economics and Law.
    8. Zhou, Qin & Luo, Yunzhao & Wang, Zhaojun, 2010. "A control chart based on likelihood ratio test for detecting patterned mean and variance shifts," Computational Statistics & Data Analysis, Elsevier, vol. 54(6), pages 1634-1645, June.
    9. Andersson, E., 2005. "On-line detection of turning points using non-parametric surveillance: The effect of the growth after the turn," Statistics & Probability Letters, Elsevier, vol. 73(4), pages 433-439, July.
    10. Assuno, Renato & Correa, Thais, 2009. "Surveillance to detect emerging space-time clusters," Computational Statistics & Data Analysis, Elsevier, vol. 53(8), pages 2817-2830, June.
    11. Frisén, Marianne, 2008. "Introduction to financial surveillance," Research Reports 2008:1, University of Gothenburg, Statistical Research Unit, School of Business, Economics and Law.
    12. Frisén, Marianne & Andersson, Eva & Pettersson, Kjell, 2008. "Semiparametric estimation of outbreak regression," Research Reports 2007:13, University of Gothenburg, Statistical Research Unit, School of Business, Economics and Law.
    13. Andersson, Eva, 2007. "Effect of dependency in systems for multivariate surveillance," Research Reports 2007:1, University of Gothenburg, Statistical Research Unit, School of Business, Economics and Law.
    14. Frisén, Marianne, 2011. "Inference Principles For Multivariate Surveillance," Research Reports 2011:5, University of Gothenburg, Statistical Research Unit, School of Business, Economics and Law.
    15. Robert Garthoff & Iryna Okhrin & Wolfgang Schmid, 2014. "Statistical surveillance of the mean vector and the covariance matrix of nonlinear time series," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 98(3), pages 225-255, July.
    16. Bock, David & Andersson, Eva & Frisén, Marianne, 2007. "Similarities and differences between statistical surveillance and certain decision rules in finance," Research Reports 2007:8, University of Gothenburg, Statistical Research Unit, School of Business, Economics and Law.
    17. He, Feng & Shu, Lianjie & Tsui, Kwok-Leung, 2014. "Adaptive CUSUM charts for monitoring linear drifts in Poisson rates," International Journal of Production Economics, Elsevier, vol. 148(C), pages 14-20.
    18. Frisén, Marianne, 2011. "Methods and evaluations for surveillance in industry, business, finance, and public health," Research Reports 2011:3, University of Gothenburg, Statistical Research Unit, School of Business, Economics and Law.
    19. Bock, David & Andersson, Eva & Frisén, Marianne, 2007. "Statistical Surveillance of Epidemics: Peak Detection of Influenza in Sweden," Research Reports 2007:6, University of Gothenburg, Statistical Research Unit, School of Business, Economics and Law.
    20. Steland, Ansgar, 2003. "Optimal sequential kernel detection for dependent processes," Technical Reports 2003,27, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    21. Bock, David & Pettersson, Kjell, 2007. "Explorative analysis of spatial aspects on the Swedish influenza data," Research Reports 2007:10, University of Gothenburg, Statistical Research Unit, School of Business, Economics and Law.
    22. Golosnoy, Vasyl & Ragulin, Sergiy & Schmid, Wolfgang, 2011. "CUSUM control charts for monitoring optimal portfolio weights," Computational Statistics & Data Analysis, Elsevier, vol. 55(11), pages 2991-3009, November.
    23. David Bock & Eva Andersson & Marianne Frisén, 2005. "Statistical surveillance of cyclical processes with application to turns in business cycles," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 24(7), pages 465-490.

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